Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 3 down vote favorite

Recently, I have been pushed toward studying analytic continuation dirichlet series with twists that are additive. These are functions $D(s) = \sum \chi(n) \frac{a_n}{n^s}$ where $a_n$ is some sequence (usually positive) and $\chi : \mathbb{Z}_{k} \to \mathbb{C}$ such that $\chi(a+b)=\chi(a)\chi(b).$

I would like to know if there is any literature on this topic available.

share|improve this question
Are you asking about Dirichlet series, or twisted Dirichlet series? My guess is both should use the same tools so you should start with usual Dirichlet series (which are covered in many analytic number theory books). If your coefficients are positive, the alternating signs might make the series converge on a bigger half plane (that's the only difference I can see so far). A good place to start might be to study the case $a_n = 1$ (which gives you the $\zeta$ function, and $L$ series in the twisted case). – Joel Cohen May 15 '11 at 1:17

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.