Jensen polynomials for the Riemann xi-function

Michael J. Griffin, Ken Ono, Larry Rolen, Jesse Thorner, Zachary Tripp, Ian Wagner

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate [Formula presented], where ζ(s) is the Riemann zeta function. The Riemann hypothesis (RH) asserts that if ξ(s)=0, then [Formula presented]. Pólya proved that RH is equivalent to the hyperbolicity of the Jensen polynomials Jd,n(X) constructed from certain Taylor coefficients of ξ(s). For each d≥1, recent work proves that Jd,n(X) is hyperbolic for sufficiently large n. In this paper, we make this result effective. Moreover, we show how the low-lying zeros of the derivatives ξ(n)(s) influence the hyperbolicity of Jd,n(X).

Original languageEnglish (US)
Article number108186
JournalAdvances in Mathematics
Volume397
DOIs
StatePublished - Mar 5 2022

Keywords

  • Jensen polynomial
  • Riemann hypothesis
  • Riemann zeta function

ASJC Scopus subject areas

  • General Mathematics

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