Elementary Deuring-Heilbronn Phenomenon
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-Vi...
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| Sprache: | eng |
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| Zusammenfassung: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.1201.0713 |