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Results tagged with zeta-functions
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user 10458
Zeta functions are typically analogues or generalizations of the Riemann zeta function. Examples include Dedekind zeta functions of number fields, and zeta functions of varieties over finite fields. They are typically initially defined as formal generating functions, but often admit analytic continuations.
14
votes
How was the importance of the zeta function discovered?
Andre Weil has an article called "Prehistory of the zeta function" (reviewed by Jutila on mathscinet). I read this article many years ago, but this is basically what I remember of its content. Apparen …
5
votes
3
answers
871
views
A question about partial Euler products
Let $K/{\mathbb Q}$ be an extension of degree $d$. Let $S$ be the set of primes $p$ which split completely in $K$. What can one say about the analytic properties of
$$
\zeta_{K, S}(s) : = \prod_{p \i …
- 1,362
6
votes
Accepted
A question about partial Euler products
This question turned out to be not too difficult. Please see
http://www.math.uic.edu/~rtakloo/euler-product.pdf
for a (casual) writeup of an answer.
Thanks for your comments and hints.
- 1,362
11
votes
2
answers
761
views
Tauberian theorem with better error term
This is a fairly vague question.
Suppose we have a sequence of positive numbers $(c_n)_n$ and we want to find an asymptotic formula for $S(x) = \sum_{n \leq X} c_n$. In favorable circumstances, stan …
- 1,362