Explicit zero-free regions for the Riemann zeta-function

DOI10.1007/s40993-023-00498-yarXiv2212.06867OpenAlexW4390813842WikidataQ130185987 ScholiaQ130185987MaRDI QIDQ6148977

Timothy S. Trudgian, Michael J. Mossinghoff, Andrew Yang

Publication date: 8 February 2024

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.06867

zbMATH Keywords

simulated annealingRiemann zeta-functionzero-free regionnon-negative trigonometric polynomials

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Trigonometric polynomials, inequalities, extremal problems (42A05) Analytic computations (11Y35)

Related Items (2)

Explicit bounds for the Riemann zeta function and a new zero-free region ⋮ Explicit bounds on \(\zeta (s)\) in the critical strip and a zero-free region

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An explicit van der Corput estimate for \(\zeta(1/2+it)\)
• An improved explicit bound on \(| \zeta(\frac{1}{2} + i t) |\)
• Explicit bounds for primes in arithmetic progressions
• An explicit result for primes between cubes
• Explicit estimates for the Riemann zeta function
• Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function
• Zur Abschätzung der Riemannschen Zetafunktion in der Nähe der Vertikalen \(\sigma = 1\)
• Counting zeros of the Riemann zeta function
• A NOTE ON KADIRI'S EXPLICIT ZERO FREE REGION FOR RIEMANN ZETA FUNCTION
• On the least prime in an arithmetic progression and estimates for the zeros of Dirichlet L-functions
• On the remainder term of the prime number formula II; On a theorem of Ingham
• Zero-free regions for the Riemann zeta function
• Zero-Free Regions for Dirichlet L-Functions, and the Least Prime in an Arithmetic Progression
• Convexité, complète monotonie et inégalités sur les fonctions zèta et gamma, sur les fonctions des opérateurs de Baskakov et sur des fonctions arithmétiques
• VINOGRADOV'S INTEGRAL AND BOUNDS FOR THE RIEMANN ZETA FUNCTION
• Sharper bounds for the Chebyshev function 𝜃(𝑥)
• The Riemann hypothesis is true up to 3·1012
• Explicit interval estimates for prime numbers
• The error term in the prime number theorem
• Computing $\pi (x)$ analytically
• Une région explicite sans zéros pour la fonction ζ de Riemann
• Explicit Bounds for Some Functions of Prime Numbers
• Primes between consecutive powers
• Sharper bounds for the error term in the prime number theorem

This page was built for publication: Explicit zero-free regions for the Riemann zeta-function