Zeros of normalized combinations of ξ(k)(s) on Re(s)=1/2

Sneha Chaubey, Amita Malik, Nicolas Robles, Alexandru Zaharescu

Research output: Contribution to journalArticle

Abstract

We consider functions of the form Fc→,a,T(s)=∑j=0 M[Formula presented]ξ(a+2j)(s), with L=log⁡[Formula presented] and cj real constants satisfying a certain constraint. We show that as T→∞ the proportion of zeros of Fc→,a,T(s) on the critical line Re(s)=1/2 tends to 1.

Original languageEnglish (US)
Pages (from-to)1771-1785
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Volume461
Issue number2
DOIs
StatePublished - May 15 2018

Keywords

  • Critical line
  • Mollifier
  • Normalized combinations
  • Proportion
  • Riemann ξ-function
  • Zeros

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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