Isolating some non-trivial zeros of zeta

DOI10.1090/mcom/3198zbMath1385.11076OpenAlexW2281218105MaRDI QIDQ2981785

David J. Platt

Publication date: 10 May 2017

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://research-information.bris.ac.uk/en/publications/2826fe29-b4d7-4911-964a-6aba9b0ce807

zbMATH Keywords

algorithmcomputation of Riemann's zeta function on the half line

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Analytic computations (11Y35)

Related Items

Jensen polynomials for holomorphic functions ⋮ Explicit zero density for the Riemann zeta function ⋮ Explicit estimates for the distribution of numbers free of large prime factors ⋮ An inequality related to the sieve of Eratosthenes ⋮ Sharper bounds for the Chebyshev function \(\psi(x)\) ⋮ Explicit zero density estimate for the Riemann zeta-function near the critical line ⋮ Explicit bounds on \(\zeta (s)\) in the critical strip and a zero-free region ⋮ Corrigendum to New bounds for $\psi (x)$ ⋮ The error term in the prime number theorem ⋮ Computing $\pi (x)$ analytically ⋮ Primes between consecutive powers ⋮ Accurate estimation of sums over zeros of the Riemann zeta-function ⋮ Explicit average orders: news and problems ⋮ Sign changes in the prime number theorem ⋮ Effective approximation of heat flow evolution of the Riemann \(\xi \) function, and a new upper bound for the de Bruijn-Newman constant ⋮ Sharper bounds for the Chebyshev function 𝜃(𝑥) ⋮ The Riemann hypothesis is true up to 3·1012

Uses Software

• mpmath
• ZetaGrid

Cites Work

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