On the nontrivial zeros of modified Epstein zeta functions

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Abstract

We study the zeros of modified Epstein zeta functions having functional equations. The result is that for any δ > 0, all but finitely many nontrivial zeros of such a function in {s ∈ ℂ: s-1/2 < δ} are simple and on the critical line. As an immediate consequence of this theorem, all but finitely many nontrivial zeros of many modified Epstein zeta functions are simple and on the critical line.

Original languageEnglish
Pages (from-to)79-81
Number of pages3
JournalComptes Rendus Mathematique
Volume342
Issue number2
DOIs
Publication statusPublished - 2006 Jan 15

Bibliographical note

Funding Information:
✩ This work was supported by grant No. R01-2005-000-10339-0 from the Basic Research Program of the Korea Science & Engineering Foundation. E-mail address: haseo@yonsei.ac.kr (H. Ki).

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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