Elementary Deuring-Heilbronn Phenomenon
Number Theory
2012-07-04 v3
Abstract
Adapting a technique of Pintz, we give an elementary demonstration of the Deuring phenomenon: a zero of \zeta(s) off the critical line gives a lower bound on L(1,\chi). The necessary tools are Dirichlet's 'method of the hyperbola', Euler summation, summation by parts, and the Polya-Vinogradov inequality.
Cite
@article{arxiv.1201.0713,
title = {Elementary Deuring-Heilbronn Phenomenon},
author = {Jeffrey Stopple},
journal= {arXiv preprint arXiv:1201.0713},
year = {2012}
}
Comments
Minor revisions per referee's comments. To appear in Acta Arithmetica