Numerical estimates on the Landau-Siegel zero and other related quantities

DOI10.1016/j.jnt.2023.04.008arXiv2301.10722OpenAlexW4378374674MaRDI QIDQ6156551

Alessandro Languasco

Publication date: 13 June 2023

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

Full work available at URL: https://arxiv.org/abs/2301.10722

zbMATH Keywords

Dirichlet \(L\)-functionsLandau-Siegel zero

Mathematics Subject Classification ID

Real zeros of (L(s, chi)); results on (L(1, chi)) (11M20) Software, source code, etc. for problems pertaining to number theory (11-04) Evaluation of number-theoretic constants (11Y60)

Related Items (2)

An explicit upper bound for \(L(1,\chi)\) when \(\chi\) is quadratic ⋮ A closed-form expression for the Euler-Kronecker constant of a quadratic field

Cites Work

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• Correction to: ``Explicit upper bound for the average number of divisors of irreducible quadratic polynomials
• Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms
• Efficient computation of the Euler-Kronecker constants of prime cyclotomic fields
• An elementary bound on Siegel zeroes
• The size of \(L(1,\chi)\) for real nonpricipal residue characters \(\chi\) with prime modulus
• Numerical verification of Littlewood's bounds for \(|L(1,\chi)|\)
• A unified strategy to compute some special functions of number-theoretic interest
• A Computational Technique for Evaluating L(1, χ) and the Class Number of a Real Quadratic Field
• Real zeros of real odd Dirichlet $L$-functions
• Accuracy of the Discrete Fourier Transform and the Fast Fourier Transform
• A fast algorithm to compute the Ramanujan-Deninger gamma function and some number-theoretic applications
• Numerical computations concerning the GRH
• Number Theory
• Algorithmic Number Theory

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