The number of zeros of the Dedekind zeta-function on the critical line

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Abstract

Erich Hecke first showed that the Dedekind zeta-function for an ideal class in an imaginary quadratic field has an infinite number of zeros on the critical line. Recently, K. Chandrasekharan and Raghavan Narasimhan proved the result for both real and imaginary quadratic fields. In this paper we give a quantitative result. Namely, let N0(T) denote the number of zeros of the Dedekind zeta-function ζK( 1 2 + it T) for 0 < t < T. Then, for every ε > 0, there exists a positive constant A such that N0(T) > AT 1 2-ε{lunate}.

Original languageEnglish (US)
Pages (from-to)1-6
Number of pages6
JournalJournal of Number Theory
Volume3
Issue number1
DOIs
StatePublished - Feb 1971

ASJC Scopus subject areas

  • Algebra and Number Theory

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