Zeros of partial sums of the Dedekind zeta function of a cyclotomic field

Andrew Ledoan, Arindam Roy, Alexandru Zaharescu

Research output: Contribution to journalArticle

Abstract

In this article, we study the zeros of the partial sums of the Dedekind zeta function of a cyclotomic field K defined by the truncated Dirichlet seriesζK,X(s)=∑{norm of matrix}a{norm of matrix}≤X1{norm of matrix}a{norm of matrix}s, where the sum is to be taken over nonzero integral ideals a of K and {norm of matrix}a{norm of matrix} denotes the absolute norm of a. Specifically, we establish the zero-free regions for ζK,X(s) and estimate the number of zeros of ζK,X(s) up to height T.

Original languageEnglish (US)
Pages (from-to)118-133
Number of pages16
JournalJournal of Number Theory
Volume136
DOIs
StatePublished - Mar 1 2014

Keywords

  • Dedekind zeta function
  • Dirichlet polynomial
  • Distribution of zeros

ASJC Scopus subject areas

  • Algebra and Number Theory

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