Elementary Deuring-Heilbronn Phenomenon

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,). The necessary tools are Dirichlet's 'method of the hyperbola', Euler summation, summation by parts, and the Polya-Vinogradov inequality.

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