part-ii/2017-66/

[tripos-comments[bot]]

Part II 2017 Further Complex Methods: Paper 1, Section II, E

https://questions.tripos.org/part-ii/2017-66/

[acornnroca]

Solution

Take collapsed Hankel contour for Re(s) > 1, then extend to not-collapsed to show analytic continuation.

Find residues to calculate $$\zeta_R(-1) = -\frac{1}{12}$$