Zeros of Dirichlet series

R. C. Vaughan

doi:10.1016/j.indag.2015.09.007

Zeros of Dirichlet series

R. C. Vaughan

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We are concerned here with Dirichlet series, which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f(s)=2^sq^1/2-sπ^s-1Γ(1-s)(sinπ/2(s+κ))f(1-s), but for which the Riemann hypothesis is false. Indeed we show that the zeros of such functions are ubiquitous in the complex plane.

Original language	English (US)
Pages (from-to)	897-909
Number of pages	13
Journal	Indagationes Mathematicae
Volume	26
Issue number	5
DOIs	https://doi.org/10.1016/j.indag.2015.09.007
State	Published - Dec 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.indag.2015.09.007

Cite this

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title = "Zeros of Dirichlet series",

abstract = "We are concerned here with Dirichlet series, which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f(s)=2sq1/2-sπs-1Γ(1-s)(sinπ/2(s+κ))f(1-s), but for which the Riemann hypothesis is false. Indeed we show that the zeros of such functions are ubiquitous in the complex plane.",

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AB - We are concerned here with Dirichlet series, which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f(s)=2sq1/2-sπs-1Γ(1-s)(sinπ/2(s+κ))f(1-s), but for which the Riemann hypothesis is false. Indeed we show that the zeros of such functions are ubiquitous in the complex plane.

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UR - https://www.scopus.com/pages/publications/84947587860#tab=citedBy

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M3 - Article

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ER -

Zeros of Dirichlet series

Abstract

All Science Journal Classification (ASJC) codes

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