Twisted second moments of the Riemann zeta-function and applications

Nicolas Robles, Arindam Roy, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


In order to compute a twisted second moment of the Riemann zeta-function, two different mollifiers, each being a combination of two different Dirichlet polynomials, were introduced separately by Bui, Conrey, and Young, and by Feng. In this article we introduce a mollifier which is a combination of four Dirichlet polynomials of different shapes. We provide an asymptotic result for the twisted second moment of ζ(s) for such choice of mollifier. A small increment on the percentage of zeros of the Riemann zeta-function on the critical line is given as an application of our results.

Original languageEnglish (US)
Article number19767
Pages (from-to)271-314
Number of pages44
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Feb 1 2016


  • Mollifier
  • Riemann zeta-function
  • Twisted second moment
  • Zeros on the critical line

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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