Elementary Deuring-Heilbronn Phenomenon

Details Elementary Deuring-Heilbronn Phenomenon Elementary Deuring-Heilbronn Phenomenon

2012-01-03

arxiv.org/abs/1201.0713v2

Mathematics

Number Theory

Minor edits, additional references

Scientific paper

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.

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