On the zeros of linear combinations of derivatives of the Riemann zeta function

K. Paolina Koutsaki, Albert Tamazyan, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, the zeros of linear combinations of the Riemann zeta function and its derivatives are studied. We establish an asymptotic formula for the number of zeros in a rectangle of height T. We also find a sharp asymptotic formula for the supremum of the real parts of zeros of such combinations in a certain family.

Original languageEnglish (US)
Pages (from-to)1703-1723
Number of pages21
JournalInternational Journal of Number Theory
Volume12
Issue number6
DOIs
StatePublished - Sep 1 2016

Keywords

  • Riemann zeta function
  • linear combination of derivatives
  • non-real zeros

ASJC Scopus subject areas

  • Algebra and Number Theory

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