Computations of the Mertens function and improved bounds on the Mertens conjecture

DOI10.1090/mcom/3275zbMath1432.11185arXiv1610.08551OpenAlexW2541102083WikidataQ123338756 ScholiaQ123338756MaRDI QIDQ4600721

Greg Hurst

Publication date: 12 January 2018

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

Full work available at URL: https://arxiv.org/abs/1610.08551

zbMATH Keywords

Mertens functionMertens conjecture

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Analytic computations (11Y35) Calculation of integer sequences (11Y55) Values of arithmetic functions; tables (11Y70)

Related Items (9)

Oscillations in the Goldbach conjecture ⋮ Bordered Hermitian matrices and sums of the Möbius function ⋮ Fake mu’s ⋮ Summing \(\mu(n)\): a faster elementary algorithm ⋮ An improved sieve of Eratosthenes ⋮ Relations among some conjectures on the Möbius function and the Riemann zeta-function ⋮ A tale of two omegas ⋮ Oscillations in weighted arithmetic sums ⋮ A singular series average and the zeros of the Riemann zeta-function

Uses Software

• fpLLL
• GitHub

Cites Work

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• H-LLL
• Disproof of the Mertens conjecture.
• Computing π(x): An analytic method
• Computing the Summation of the Möbius Function
• On the Order of the Mertens Function
• The distribution of the summatory function of the Möbius function
• Computing $\pi (x)$ analytically
• Linear relations of zeroes of the zeta-function
• Oscillation Theorems of Arithmetical Functions
• On Two Conjectures in the Theory of Numbers

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