Zeros of Dirichlet series

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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.

Original languageEnglish (US)
Pages (from-to)897-909
Number of pages13
JournalIndagationes Mathematicae
Volume26
Issue number5
DOIs
StatePublished - Dec 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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