Note on the number of zeros of ζ(k)(s)

Research output: Contribution to journalArticlepeer-review

Abstract

Assuming the Riemann hypothesis, we prove that Nk(T)=T2πlogT4πe+Ok(logTloglogT),where Nk(T) is the number of zeros of ζ(k)(s) in the region 0 < Is≤ T. We further apply our method and obtain a zero counting formula for the derivative of Selberg zeta functions, improving earlier work of Luo (Am J Math 127(5):1141–1151, 2005).

Original languageEnglish
Pages (from-to)661-672
Number of pages12
JournalRamanujan Journal
Volume55
Issue number2
DOIs
Publication statusPublished - Jun 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Note on the number of zeros of ζ<sup>(</sup><sup>k</sup><sup>)</sup>(s)'. Together they form a unique fingerprint.

Cite this