Smooth L2 distances and zeros of approximations of Dedekind zeta functions

Junxian Li, Maria Monica Nastasescu, Arindam Roy*, Alexandru Zaharescu

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We consider a family of approximations of the Dedekind zeta function ζK(s) of a number field K/ Q. Weighted L2-norms of the difference of two such approximations of ζK(s) are computed. We work with a weight which is a compactly supported smooth function. Mean square estimates for the difference of approximations of ζK(s) can be obtained from such weighted L2-norms. Some results on the location of zeros of a family of approximations of Dedekind zeta functions are also derived. These results extend results of Gonek and Montgomery on families of approximations of the Riemann zeta-function.

Original languageEnglish (US)
Pages (from-to)195-223
Number of pages29
JournalManuscripta Mathematica
Volume154
Issue number1-2
DOIs
StatePublished - Sep 1 2017

Keywords

  • 11R42
  • Primary 11M41

ASJC Scopus subject areas

  • Mathematics(all)

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