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

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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
Issue number2
Publication statusPublished - Jun 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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