An explicit zero-free region for the Dirichlet L-functions

Details An explicit zero-free region for the Dirichlet L-functions An explicit zero-free region for the Dirichlet L-functions

2005-10-26

arxiv.org/abs/math/0510570v1

Mathematics

Number Theory

32 pages

Scientific paper

In this article we give an effective zero free region for the Dirichlet L-functions associated to a given integer $q$. We prove that the function $\prod_{\chi({\rm mod} q)}L(s,\chi)$ never vanishes in the region $\sigma \ge 1- \frac1{6.2443 \log q|t|}, |t|> 1$ and it possesses at most one exceptional zero in the region $\sigma \ge 1- \frac1{6.3970 \log q}, |t|\le 1.$ Such a zero, if it exists, is real, simple and corresponds to a real non-principal character modulo $q$. In addition, we show the region $ \sigma \ge 1-\frac1{4.0904 \log q}, t=0$ contains at most one zero.

Affiliated with

Also associated with

No associations

Rating

An explicit zero-free region for the Dirichlet L-functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An explicit zero-free region for the Dirichlet L-functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An explicit zero-free region for the Dirichlet L-functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-555792