1
vote
1answer
545 views

An integral representation of the Riemann zeta function

I am referring to the equality in equation $3.29$ (page 12) and $4.20$ (page 17) in this paper. I am unable to recognize where this comes from or what is the general expression for values other than ...
9
votes
1answer
518 views

Euler product over primes congruent to 3 mod 4

I'm a string theorist and I have come across the following expression in a computation I'm doing (involving a sum over inequivalent Lens spaces): $$\widehat{\zeta}(s)=\prod_{\mathrm{primes}\ p\equiv ...
6
votes
2answers
495 views

Poles of Kloosterman Zeta Function

I am a string theorist who has encountered the following number theory problem in my research. Consider the sums $$Z_+(s) = \sum_{p=1}^\infty p^{-s} S(1,1; p)$$ and $$Z_-(s) = \sum_{p=1}^\infty ...