Tagged Questions
5
votes
1answer
126 views
Exponentiation of a Dirichlet series
I'm trying to understand a proof in Chandrasekharan's Introduction to Analytic Number Theory. Specifically, the proof of the lemma on p.118 before Dirichlet's theorem on primes in arithmetic ...
11
votes
2answers
334 views
regularity of root spacing of $G(z)=\sum\limits_{n=1}^{\infty} \frac{e^{-n^{2}}}{n^{z}}$
Define, on $\mathbb{C}$:
$$G(z)=\sum_{n=1}^{\infty} \frac{e^{-n^{2}}}{n^{z}}$$
A domain colored portrait of $G(z)$ (boxes are supposed to be negative signs):
suggests that the roots of $G(z)$ are ...
