This article is cited in 2 papers

Short notes

The Dirchlet $L$-function does not vanish for $s=1$

V. N. Chubarikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A new proof of Dirichlet's theorem that a Dirichlet $L$-series for a prime modulo $q\equiv 3\pmod 4$ with a real character does not vanish is given.

Key words: Dirichlet's series, Gaussian sum, “saw-tooth” function.

UDC: 511

Received: 27.06.2014

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2015, 70:2, 96–98

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