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 language | English (US) |
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Article number | 108186 |
Journal | Advances in Mathematics |
Volume | 397 |
DOIs | |
State | Published - Mar 5 2022 |
Keywords
- Jensen polynomial
- Riemann hypothesis
- Riemann zeta function
ASJC Scopus subject areas
- General Mathematics