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arXiv · 1201.0713

Elementary Deuring-Heilbronn Phenomenon

Jeffrey Stopple
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Abstract

Adapting a technique of Pintz, we give an elementary demonstration of the Deuring phenomenon: a zero of ζ(s) off the critical line gives a lower bound on L(1,χ). The necessary tools are Dirichlet's 'method of the hyperbola', Euler summation, summation by parts, and the Polya-Vinogradov inequality.

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Jeffrey Stopple. 2012-07-02. Elementary Deuring-Heilbronn Phenomenon. https://arxiv.org/abs/1201.0713

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