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@book {Alaca-Williams,
AUTHOR = {Alaca, \c{S}aban and Williams, Kenneth S.},
TITLE = {Introductory algebraic number theory},
PUBLISHER = {Cambridge University Press, Cambridge},
YEAR = {2004},
PAGES = {xviii+428},
ISBN = {0-521; 0-521-54011-9},
MRNUMBER = {2031707},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Apostol-analytic,
AUTHOR = {Apostol, Tom M.},
TITLE = {Introduction to analytic number theory},
NOTE = {Undergraduate Texts in Mathematics},
PUBLISHER = {Springer-Verlag, New York-Heidelberg},
YEAR = {1976},
PAGES = {xii+338},
MRNUMBER = {0434929},
URL = {https://doi.org/10.1007/978-1-4757-5579-4}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Artin-Galois,
AUTHOR = {Artin, Emil},
TITLE = {Galois theory},
EDITION = {second},
NOTE = {Edited and with a supplemental chapter by Arthur N. Milgram},
PUBLISHER = {Dover Publications, Inc., Mineola, NY},
YEAR = {1998},
PAGES = {iv+82},
ISBN = {0-486-62342-4},
MRNUMBER = {1616156},
key = {Artin-Galois}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Atiyah-Macdonald,
AUTHOR = {Atiyah, Michael F. and Macdonald, Ian G.},
TITLE = {Introduction to commutative algebra},
PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
Mills, Ont.},
YEAR = {1969},
PAGES = {ix+128},
MRNUMBER = {0242802},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Ayoub-Chowla,
AUTHOR = {Ayoub, Raymond G. and Chowla, Sarvadaman},
TITLE = {On {E}uler's polynomial},
JOURNAL = {J. Number Theory},
FJOURNAL = {Journal of Number Theory},
VOLUME = {13},
YEAR = {1981},
NUMBER = {4},
PAGES = {443--445},
ISSN = {0022-314X},
MRCLASS = {10A25 (12A25)},
MRNUMBER = {642919},
DOI = {10.1016/0022-314X(81)90035-4},
URL = {https://doi.org/10.1016/0022-314X(81)90035-4},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Baker-1990,
AUTHOR = {Baker, Alan},
TITLE = {Transcendental number theory},
SERIES = {Cambridge Mathematical Library},
EDITION = {Second},
PUBLISHER = {Cambridge University Press, Cambridge},
YEAR = {1990},
PAGES = {x+165},
ISBN = {0-521-39791-X},
MRCLASS = {11Jxx (11J81)},
MRNUMBER = {1074572},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Belabas-1997,
AUTHOR = {Belabas, Karim},
TITLE = {A fast algorithm to compute cubic fields},
JOURNAL = {Math. Comp.},
FJOURNAL = {Mathematics of Computation},
VOLUME = {66},
YEAR = {1997},
NUMBER = {219},
PAGES = {1213--1237},
ISSN = {0025-5718},
MRCLASS = {11Y40 (11R16)},
MRNUMBER = {1415795},
DOI = {10.1090/S0025-5718-97-00846-6},
URL = {https://doi.org/10.1090/S0025-5718-97-00846-6},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Belabas-Bhargava-Pomerance,
AUTHOR = {Belabas, Karim and Bhargava, Manjul and Pomerance, Carl},
TITLE = {Error estimates for the {D}avenport-{H}eilbronn theorems},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {153},
YEAR = {2010},
NUMBER = {1},
PAGES = {173--210},
ISSN = {0012-7094},
MRCLASS = {11R29 (11R11 11R16 11R45)},
MRNUMBER = {2641942},
DOI = {10.1215/00127094-2010-007},
URL = {https://doi.org/10.1215/00127094-2010-007},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Bhargava-2005,
AUTHOR = {Bhargava, Manjul},
TITLE = {The density of discriminants of quartic rings and fields},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {162},
YEAR = {2005},
NUMBER = {2},
PAGES = {1031--1063},
ISSN = {0003-486X},
MRCLASS = {11R45 (11R16 11R29)},
MRNUMBER = {2183288},
DOI = {10.4007/annals.2005.162.1031},
URL = {https://doi.org/10.4007/annals.2005.162.1031},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Bhargava-2010,
AUTHOR = {Bhargava, Manjul},
TITLE = {The density of discriminants of quintic rings and fields},
JOURNAL = {Ann. of Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {172},
YEAR = {2010},
NUMBER = {3},
PAGES = {1559--1591},
ISSN = {0003-486X},
MRCLASS = {11R29 (11R21 11R45)},
MRNUMBER = {2745272},
DOI = {10.4007/annals.2010.172.1559},
URL = {https://doi.org/10.4007/annals.2010.172.1559},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@proceedings {Bloch-Kato-for-riemann-zeta,
TITLE = {The {B}loch-{K}ato conjecture for the {R}iemann zeta function},
SERIES = {London Mathematical Society Lecture Note Series},
VOLUME = {418},
BOOKTITLE = {Proceedings of the workshop held at the {I}ndian {I}nstitute
of {S}cience {E}ducation and {R}esearch ({IISER}), {P}une,
{J}uly 2012},
EDITOR = {Coates, John and Raghuram, A. and Saikia, Anupam and Sujatha, R.},
PUBLISHER = {Cambridge University Press, Cambridge},
YEAR = {2015},
PAGES = {ix+305},
ISBN = {978-1-107-49296-7},
MRCLASS = {11-06 (11M06)},
MRNUMBER = {3410209},
DOI = {10.1017/CBO9781316163757},
URL = {https://doi.org/10.1017/CBO9781316163757},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Borevich-Shafarevich,
AUTHOR = {Borevich, A. I. and Shafarevich, I. R.},
TITLE = {Number theory},
SERIES = {Translated from the Russian by Newcomb Greenleaf. Pure and
Applied Mathematics, Vol. 20},
PUBLISHER = {Academic Press, New York-London},
YEAR = {1966},
PAGES = {x+435},
MRNUMBER = {0195803},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@incollection {Bosma-deSmit-2002,
AUTHOR = {Bosma, Wieb and de Smit, Bart},
TITLE = {On arithmetically equivalent number fields of small degree},
BOOKTITLE = {Algorithmic number theory ({S}ydney, 2002)},
SERIES = {Lecture Notes in Comput. Sci.},
VOLUME = {2369},
PAGES = {67--79},
PUBLISHER = {Springer, Berlin},
YEAR = {2002},
MRNUMBER = {2041074},
DOI = {10.1007/3-540-45455-1_6},
URL = {https://doi.org/10.1007/3-540-45455-1_6},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Buchmann-Williams-1987,
AUTHOR = {Buchmann, Johannes and Williams, Hugh C.},
TITLE = {On principal ideal testing in algebraic number fields},
JOURNAL = {J. Symbolic Comput.},
FJOURNAL = {Journal of Symbolic Computation},
VOLUME = {4},
YEAR = {1987},
NUMBER = {1},
PAGES = {11--19},
ISSN = {0747-7171},
MRCLASS = {11R29 (11Y40)},
MRNUMBER = {908408},
DOI = {10.1016/S0747-7171(87)80049-4},
URL = {https://doi.org/10.1016/S0747-7171(87)80049-4},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Carlitz-1960,
AUTHOR = {Carlitz, Leonhard},
TITLE = {A characterization of algebraic number fields with class number two},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {11},
YEAR = {1960},
PAGES = {391--392},
ISSN = {0002-9939},
MRCLASS = {12.0},
MRNUMBER = {111741},
DOI = {10.1090/S0002-9939-1960-0111741-2},
URL = {https://doi.org/10.1090/S0002-9939-1960-0111741-2},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@proceedings {Cassels-Frohlich,
TITLE = {Algebraic number theory},
EDITION = {Second},
BOOKTITLE = {Proceedings of an instructional conference organized by the
{L}ondon {M}athematical {S}ociety (a {NATO} {A}dvanced {S}tudy
{I}nstitute) with the support of the {I}nternational
{M}athematical {U}nion},
EDITOR = {Cassels, J. W. S. and Fr\"{o}hlich, Albrecht},
NOTE = {Papers from the conference held at the University of Sussex,
Brighton, September 1--17, 1965,
Including a list of errata},
PUBLISHER = {London Mathematical Society, London},
YEAR = {2010},
PAGES = {xxiv + 366},
ISBN = {978-0-95027-342-6},
MRCLASS = {00B25 (11-06 11Rxx)},
MRNUMBER = {3618860},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Claborn-1966,
AUTHOR = {Claborn, Luther},
TITLE = {Every abelian group is a class group},
JOURNAL = {Pacific J. Math.},
FJOURNAL = {Pacific Journal of Mathematics},
VOLUME = {18},
YEAR = {1966},
PAGES = {219--222},
ISSN = {0030-8730},
MRNUMBER = {195889},
URL = {http://projecteuclid.org/euclid.pjm/1102994263},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc {Clark-CA,
AUTHOR = {Clark, Pete L.},
TITLE = {Commutative Algebra},
KEY = {Clark-CA},
URL = {http://math.uga.edu/~pete/integral2015.pdf}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Cohen-GTM138,
AUTHOR = {Cohen, Henri},
TITLE = {A course in computational algebraic number theory},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {138},
PUBLISHER = {Springer-Verlag, Berlin},
YEAR = {1993},
PAGES = {xii+534},
ISBN = {3-540-55640-0},
MRNUMBER = {1228206},
DOI = {10.1007/978-3-662-02945-9},
URL = {https://doi.org/10.1007/978-3-662-02945-9},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Cohen-GTM239,
AUTHOR = {Cohen, Henri},
TITLE = {Number theory. {V}ol. {I}. {T}ools and {D}iophantine equations},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {239},
PUBLISHER = {Springer, New York},
YEAR = {2007},
PAGES = {xxiv+650},
ISBN = {978-0-387-49922-2},
MRNUMBER = {2312337},
DOI = {https://doi.org/10.1007/978-0-387-49923-9}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@incollection {Cohen-Lenstra-1984,
AUTHOR = {Cohen, Henri and Lenstra, Jr., Hendrik W.},
TITLE = {Heuristics on class groups of number fields},
BOOKTITLE = {Number theory, {N}oordwijkerhout 1983 ({N}oordwijkerhout, 1983)},
SERIES = {Lecture Notes in Math.},
VOLUME = {1068},
PAGES = {33--62},
PUBLISHER = {Springer, Berlin},
YEAR = {1984},
MRCLASS = {11R29 (13C13)},
MRNUMBER = {756082},
DOI = {10.1007/BFb0099440},
URL = {https://doi.org/10.1007/BFb0099440},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Cohn-2006,
AUTHOR = {Cohn, Henry},
TITLE = {A short proof of the simple continued fraction expansion of {$e$}},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {American Mathematical Monthly},
VOLUME = {113},
YEAR = {2006},
NUMBER = {1},
PAGES = {57--62},
ISSN = {0002-9890},
MRNUMBER = {2202921},
DOI = {10.2307/27641837},
URL = {https://arxiv.org/abs/math/0601660}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Cox-2013,
AUTHOR = {Cox, David A.},
TITLE = {Primes of the form {$x^2 + ny^2$}},
SERIES = {Pure and Applied Mathematics (Hoboken)},
EDITION = {Second},
NOTE = {Fermat, class field theory, and complex multiplication},
PUBLISHER = {John Wiley \& Sons, Inc., Hoboken, NJ},
YEAR = {2013},
PAGES = {xviii+356},
ISBN = {978-1-118-39018-4},
MRNUMBER = {3236783},
DOI = {10.1002/9781118400722},
URL = {https://doi.org/10.1002/9781118400722}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {deSmit-Perlis-1994,
AUTHOR = {de Smit, Bart and Perlis, Robert},
TITLE = {Zeta functions do not determine class numbers},
JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
FJOURNAL = {American Mathematical Society. Bulletin. New Series},
VOLUME = {31},
YEAR = {1994},
NUMBER = {2},
PAGES = {213--215},
ISSN = {0273-0979},
MRNUMBER = {1260520},
DOI = {10.1090/S0273-0979-1994-00520-8},
URL = {https://doi.org/10.1090/S0273-0979-1994-00520-8},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc{Everiste-ANT,
author = {Evertse, Jan-Hendrik and Sofos, Efthymios},
title = {Analytic Number Theory},
note = {Apuntes en línea},
year = {2016},
url = {http://www.math.leidenuniv.nl/~evertse/ant.shtml}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Edwards-1975,
AUTHOR = {Edwards, Harold M.},
TITLE = {The background of {K}ummer's proof of {F}ermat's last theorem
for regular primes},
JOURNAL = {Arch. History Exact Sci.},
FJOURNAL = {Archive for History of Exact Sciences},
VOLUME = {14},
YEAR = {1975},
NUMBER = {3},
PAGES = {219--236},
ISSN = {0003-9519},
MRNUMBER = {0472364},
DOI = {10.1007/BF00327448},
URL = {https://doi.org/10.1007/BF00327448},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Edwards-1977,
AUTHOR = {Edwards, Harold M.},
TITLE = {Postscript to: ``{T}he background of {K}ummer's proof of
{F}ermat's last theorem for regular primes'' ({A}rch.
{H}istory {E}xact {S}ci. {\bf 14} (1975), no. 3, 219--236)},
JOURNAL = {Arch. History Exact Sci.},
FJOURNAL = {Archive for History of Exact Sciences},
VOLUME = {17},
YEAR = {1977},
NUMBER = {4},
PAGES = {381--394},
ISSN = {0003-9519},
MRNUMBER = {0472365},
DOI = {10.1007/BF00328877},
URL = {https://doi.org/10.1007/BF00328877},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Edwards-1996,
AUTHOR = {Edwards, Harold M.},
TITLE = {Fermat's last theorem},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {50},
NOTE = {A genetic introduction to algebraic number theory,
Corrected reprint of the 1977 original},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {1996},
PAGES = {xvi+410},
ISBN = {0-387-90230-9; 0-387-95002-8},
MRNUMBER = {1416327},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Eisenbud-Harris,
author = {Eisenbud, David and Harris, Joe},
isbn = {978-0-387-98638-8},
pages = {300+XII},
publisher = {Springer-Verlag},
title = {The Geometry of Schemes},
year = 2000,
series = {Graduate Texts in Mathematics},
volume = {197},
doi = {10.1007/b97680},
url = {http://doi.org/10.1007/b97680},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@incollection {Elstrodt-2007,
AUTHOR = {Elstrodt, J\"{u}rgen},
TITLE = {The life and work of {G}ustav {L}ejeune {D}irichlet (1805--1859)},
BOOKTITLE = {Analytic number theory},
SERIES = {Clay Math. Proc.},
VOLUME = {7},
PAGES = {1--37},
PUBLISHER = {Amer. Math. Soc., Providence, RI},
YEAR = {2007},
MRCLASS = {01A70 (01A55 11-03)},
MRNUMBER = {2362192},
DOI = {10.1070/rm1983v038n01abeh003384},
URL = {https://doi.org/10.1070/rm1983v038n01abeh003384},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {E461,
author = {Euler, Leonhard},
title = {Extrait d'un lettre de {M}. {E}uler le {P}ere \`a {M}. {B}ernoulli concernant le {M}\'emoire imprim\'e parmi ceux de 1771, p. 318},
year = {1774},
journal = {Nouveaux {M}émoires de l'académie royale des sciences de {B}erlin},
pages = {35--36},
url = {https://scholarlycommons.pacific.edu/euler-works/461},
key = {E461}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc {E792,
author = {Euler, Leonhard},
title = {Tractatus de numerorum doctrina capita {XVI}, quae supersunt},
year = {1849},
url = {https://scholarlycommons.pacific.edu/euler-works/792},
key = {E792}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Frohlich-Taylor,
AUTHOR = {Fr\"{o}hlich, Albrecht and Taylor, Martin J.},
TITLE = {Algebraic number theory},
SERIES = {Cambridge Studies in Advanced Mathematics},
VOLUME = {27},
PUBLISHER = {Cambridge University Press, Cambridge},
YEAR = {1993},
PAGES = {xiv+355},
ISBN = {0-521-43834-9},
MRNUMBER = {1215934},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc {Futterer-Villanueva,
author = {F\"utterer, Michael and Villanueva, Jos\'e},
title = {Torres infinitas sorprendentes. {U}na introducción a la teoría de {I}wasawa},
year = {2020},
url = {https://arxiv.org/abs/2008.13375}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Goldfeld-1985,
AUTHOR = {Goldfeld, Dorian},
TITLE = {Gauss's class number problem for imaginary quadratic fields},
JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
FJOURNAL = {American Mathematical Society. Bulletin. New Series},
VOLUME = {13},
YEAR = {1985},
NUMBER = {1},
PAGES = {23--37},
ISSN = {0273-0979},
MRCLASS = {11R29 (01A55 01A60 11-03 11G05)},
MRNUMBER = {788386},
DOI = {10.1090/S0273-0979-1985-15352-2},
URL = {https://doi.org/10.1090/S0273-0979-1985-15352-2},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book{Gortz-Wedhorn,
title = {Algebraic Geometry {I}: Schemes. {W}ith Examples and Exercises},
author = {G\"{o}rtz, Ulrich and Wedhorn, Torsten},
pages = {615+IV},
year = {2010},
publisher = {Vieweg+Teubner Verlag},
url = {http://doi.org/10.1007/978-3-8348-9722-0}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Grosswald-1985,
AUTHOR = {Grosswald, Emil},
TITLE = {Representations of integers as sums of squares},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {1985},
PAGES = {xi+251},
ISBN = {0-387-96126-7},
MRCLASS = {11-01 (11D85 11E25 11P05)},
MRNUMBER = {803155},
DOI = {10.1007/978-1-4613-8566-0},
URL = {https://doi.org/10.1007/978-1-4613-8566-0},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Hlawka-Taschner-Schoissengeier,
AUTHOR = {Hlawka, Edmund and Taschner, Rudolf and Schoi\ss{}engeier, Johannes},
TITLE = {Geometric and Analytic Number Theory},
SERIES = {Universitext},
PUBLISHER = {Springer, Berlin Heidelberg},
NOTE = {Translated from the 1986 German edition by Charles Thomas},
YEAR = {1991},
PAGES = {X+238},
ISBN = {978-3-540-52016-0},
MRNUMBER = {1123023},
DOI = {10.1007/978-3-642-75306-0},
URL = {https://doi.org/10.1007/978-3-642-75306-0}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Ireland-Rosen,
AUTHOR = {Ireland, Kenneth and Rosen, Michael},
TITLE = {A classical introduction to modern number theory},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {84},
EDITION = {Second},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {1990},
PAGES = {xiv+389},
ISBN = {0-387-97329-X},
MRNUMBER = {1070716},
DOI = {10.1007/978-1-4757-2103-4},
URL = {https://doi.org/10.1007/978-1-4757-2103-4}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Kato-NT-2,
AUTHOR = {Kato, Kazuya and Kurokawa, Nobushige and Saito, Takeshi},
TITLE = {Number theory. 2},
SERIES = {Translations of Mathematical Monographs},
VOLUME = {240},
NOTE = {Introduction to class field theory,
Translated from the 1998 Japanese original by Masato Kuwata
and Katsumi Nomizu,
Iwanami Series in Modern Mathematics},
PUBLISHER = {American Mathematical Society, Providence, RI},
YEAR = {2011},
PAGES = {viii+240},
ISBN = {978-0-8218-1355-3},
MRNUMBER = {2817199},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc {KCd-Galois,
author = {Conrad, Keith},
title = {Fields and Galois theory},
note = {Apuntes en l\'inea},
url = {https://kconrad.math.uconn.edu/blurbs/},
key = {KCd-Galois}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc {KCd-Selmer,
author = {Conrad, Keith},
title = {The Galois group of {$x^n - x - 1$} OVER $\mathbb{Q}$},
note = {Apuntes en l\'inea},
url = {https://kconrad.math.uconn.edu/blurbs/},
key = {KCd-Selmer}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Khinchin-1997,
AUTHOR = {Khinchin, A. Ya.},
TITLE = {Continued fractions},
EDITION = {Russian},
NOTE = {With a preface by B. V. Gnedenko,
Reprint of the 1964 translation},
PUBLISHER = {Dover Publications, Inc., Mineola, NY},
YEAR = {1997},
PAGES = {xii+95},
ISBN = {0-486-69630-8},
MRCLASS = {11A55 (01A75 11-03 11J70)},
MRNUMBER = {1451873},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@incollection {Kontsevich-Zagier,
AUTHOR = {Kontsevich, Maxim and Zagier, Don},
TITLE = {Periods},
BOOKTITLE = {Mathematics unlimited---2001 and beyond},
PAGES = {771--808},
PUBLISHER = {Springer, Berlin},
YEAR = {2001},
MRCLASS = {11-02 (11F67 11G40 11G55)},
MRNUMBER = {1852188},
url = {https://doi.org/10.1007/978-3-642-56478-9_39},
doi = {10.1007/978-3-642-56478-9_39}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Lang-Algebra,
AUTHOR = {Lang, Serge},
TITLE = {Algebra},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {211},
EDITION = {third},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {2002},
PAGES = {xvi+914},
ISBN = {0-387-95385-X},
MRNUMBER = {1878556},
DOI = {10.1007/978-1-4613-0041-0},
URL = {https://doi.org/10.1007/978-1-4613-0041-0}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Lang-ANT,
AUTHOR = {Lang, Serge},
TITLE = {Algebraic number theory},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {110},
EDITION = {Second},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {1994},
PAGES = {xiv+357},
ISBN = {0-387-94225-4},
MRNUMBER = {1282723},
DOI = {10.1007/978-1-4612-0853-2},
URL = {https://doi.org/10.1007/978-1-4612-0853-2}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Lenstra-1992,
AUTHOR = {Lenstra, Jr., Hendrik W.},
TITLE = {Algorithms in algebraic number theory},
JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
FJOURNAL = {American Mathematical Society. Bulletin. New Series},
VOLUME = {26},
YEAR = {1992},
NUMBER = {2},
PAGES = {211--244},
ISSN = {0273-0979},
MRNUMBER = {1129315},
DOI = {10.1090/S0273-0979-1992-00284-7},
URL = {https://doi.org/10.1090/S0273-0979-1992-00284-7}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Lenstra-Stevenhagen-1996,
AUTHOR = {Stevenhagen, Peter and Lenstra, Jr., Hendrik W.},
TITLE = {Chebotar\"{e}v and his density theorem},
JOURNAL = {Math. Intelligencer},
FJOURNAL = {The Mathematical Intelligencer},
VOLUME = {18},
YEAR = {1996},
NUMBER = {2},
PAGES = {26--37},
ISSN = {0343-6993},
MRNUMBER = {1395088},
DOI = {10.1007/BF03027290},
URL = {https://doi.org/10.1007/BF03027290}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Lorenzini-1996,
AUTHOR = {Lorenzini, Dino},
TITLE = {An invitation to arithmetic geometry},
SERIES = {Graduate Studies in Mathematics},
VOLUME = {9},
PUBLISHER = {American Mathematical Society, Providence, RI},
YEAR = {1996},
PAGES = {xvi+397},
ISBN = {0-8218-0267-4},
MRNUMBER = {1376367},
DOI = {10.1090/gsm/009},
URL = {https://doi.org/10.1090/gsm/009},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Marcus-NF,
AUTHOR = {Marcus, Daniel A.},
TITLE = {Number fields},
SERIES = {Universitext},
NOTE = {Second edition of [ MR0457396],
With a foreword by Barry Mazur},
PUBLISHER = {Springer, Cham},
YEAR = {2018},
PAGES = {xviii+203},
ISBN = {978-3-319-90232-6; 978-3-319-90233-3},
MRNUMBER = {3822326},
DOI = {10.1007/978-3-319-90233-3},
URL = {https://doi.org/10.1007/978-3-319-90233-3},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Morandi-GTM167,
AUTHOR = {Morandi, Patrick},
TITLE = {Field and {G}alois theory},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {167},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {1996},
PAGES = {xvi+281},
ISBN = {0-387-94753-1},
MRNUMBER = {1410264},
DOI = {10.1007/978-1-4612-4040-2},
URL = {https://doi.org/10.1007/978-1-4612-4040-2}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Moser-1951,
AUTHOR = {Moser, Leo},
TITLE = {A theorem on quadratic residues},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {2},
YEAR = {1951},
PAGES = {503--504},
ISSN = {0002-9939},
MRCLASS = {10.0X},
MRNUMBER = {41159},
DOI = {10.2307/2031783},
URL = {https://doi.org/10.2307/2031783},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@proceedings {Motives-I,
TITLE = {Motives},
SERIES = {Proceedings of Symposia in Pure Mathematics},
VOLUME = {55},
BOOKTITLE = {Proceedings of the {AMS}-{IMS}-{SIAM} {J}oint {S}ummer
{R}esearch {C}onference held at the {U}niversity of
{W}ashington, {S}eattle, {W}ashington, {J}uly 20--{A}ugust 2,
1991},
EDITOR = {Jannsen, Uwe and Kleiman, Steven and Serre, Jean-Pierre},
PUBLISHER = {American Mathematical Society, Providence, RI},
YEAR = {1994},
PAGES = {xiv+747},
ISBN = {0-8218-1636-5},
MRCLASS = {11-06 (19-06)},
MRNUMBER = {1265518},
DOI = {10.1090/pspum/055.1},
URL = {https://doi.org/10.1090/pspum/055.1},
key = {Motives-I}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Nagell-1964,
AUTHOR = {Nagell, Trygve},
TITLE = {Introduction to number theory},
SERIES = {Second edition},
PUBLISHER = {Chelsea Publishing Co., New York},
YEAR = {1964},
PAGES = {309},
MRNUMBER = {0174513}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Neukirch-ANT,
AUTHOR = {Neukirch, J\"{u}rgen},
TITLE = {Algebraic number theory},
SERIES = {Grundlehren der Mathematischen Wissenschaften [Fundamental
Principles of Mathematical Sciences]},
VOLUME = {322},
NOTE = {Translated from the 1992 German original and with a note by
Norbert Schappacher,
With a foreword by G. Harder},
PUBLISHER = {Springer-Verlag, Berlin},
YEAR = {1999},
PAGES = {xviii+571},
ISBN = {3-540-65399-6},
MRNUMBER = {1697859},
DOI = {10.1007/978-3-662-03983-0},
URL = {https://doi.org/10.1007/978-3-662-03983-0},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Olds-1970,
AUTHOR = {Olds, Carl D.},
TITLE = {The {S}imple {C}ontinued {F}raction {E}xpansion of {$e$}},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {American Mathematical Monthly},
VOLUME = {77},
YEAR = {1970},
NUMBER = {9},
PAGES = {968--974},
ISSN = {0002-9890},
MRNUMBER = {1536091},
DOI = {10.2307/2318113},
URL = {https://www.maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Olds.pdf}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Osada-1987,
AUTHOR = {Osada, Hiroyuki},
TITLE = {The {G}alois groups of the polynomials {$X^n+aX^\ell+b$}},
JOURNAL = {J. Number Theory},
FJOURNAL = {Journal of Number Theory},
VOLUME = {25},
YEAR = {1987},
NUMBER = {2},
PAGES = {230--238},
ISSN = {0022-314X},
MRCLASS = {11R09 (12E10 12F10)},
MRNUMBER = {873881},
DOI = {10.1016/0022-314X(87)90029-1},
URL = {https://doi.org/10.1016/0022-314X(87)90029-1},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Perlis-1977,
AUTHOR = {Perlis, Robert},
TITLE = {On the equation {$\zeta _{K}(s)=\zeta _{K'}(s)$}},
JOURNAL = {J. Number Theory},
FJOURNAL = {Journal of Number Theory},
VOLUME = {9},
YEAR = {1977},
NUMBER = {3},
PAGES = {342--360},
ISSN = {0022-314X},
MRCLASS = {12A70 (20D10)},
MRNUMBER = {447188},
DOI = {10.1016/0022-314X(77)90070-1},
URL = {https://doi.org/10.1016/0022-314X(77)90070-1},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Pohst-Zassenhaus,
AUTHOR = {Pohst, Michael and Zassenhaus, Hans},
TITLE = {Algorithmic algebraic number theory},
SERIES = {Encyclopedia of Mathematics and its Applications},
VOLUME = {30},
NOTE = {Revised reprint of the 1989 original},
PUBLISHER = {Cambridge University Press, Cambridge},
YEAR = {1997},
PAGES = {xiv+499},
ISBN = {0-521-59669-6},
MRNUMBER = {1483321},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {van-der-Poorten-1978,
AUTHOR = {van der Poorten, Alfred},
TITLE = {A proof that {E}uler missed{$\ldots $}{A}p\'ery's proof of the
irrationality of {$\zeta (3)$}},
NOTE = {An informal report},
JOURNAL = {Math. Intelligencer},
FJOURNAL = {The Mathematical Intelligencer},
VOLUME = {1},
YEAR = {1979},
NUMBER = {4},
PAGES = {195--203},
ISSN = {0343-6993},
MRCLASS = {10H05 (10F35)},
MRNUMBER = {547748},
DOI = {10.1007/BF03028234},
URL = {http://dx.doi.org/10.1007/BF03028234},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Reid-UCA,
AUTHOR = {Reid, Miles},
TITLE = {Undergraduate commutative algebra},
SERIES = {London Mathematical Society Student Texts},
VOLUME = {29},
PUBLISHER = {Cambridge University Press, Cambridge},
YEAR = {1995},
PAGES = {xiv+153},
ISBN = {0-521-45255-4},
MRNUMBER = {1458066},
DOI = {10.1017/CBO9781139172721},
URL = {https://doi.org/10.1017/CBO9781139172721},
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Ribenboim-FLT,
AUTHOR = {Ribenboim, Paulo},
TITLE = {Fermat's last theorem for amateurs},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {1999},
PAGES = {xiv+407},
ISBN = {0-387-98508-5},
MRNUMBER = {1719329},
doi = {10.1007/b97437},
url = {https://doi.org/10.1007/b97437}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@book {Ribenboim-Friends,
AUTHOR = {Ribenboim, Paulo},
TITLE = {My numbers, my friends},
NOTE = {Popular lectures on number theory},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {2000},
PAGES = {xii+375},
ISBN = {0-387-98911-0},
MRCLASS = {11-01},
MRNUMBER = {1761897},
doi = {10.1007/b98892},
url = {https://doi.org/10.1007/b98892}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article {Rivoal-2000,
AUTHOR = {Rivoal, Tanguy},
TITLE = {La fonction z\^{e}ta de {R}iemann prend une infinit\'{e} de valeurs
irrationnelles aux entiers impairs},
JOURNAL = {C. R. Acad. Sci. Paris S\'{e}r. I Math.},
FJOURNAL = {Comptes Rendus de l'Acad\'{e}mie des Sciences. S\'{e}rie I.
Math\'{e}matique},