Explicit upper bounds for the remainder term in the divisor problem

DOI10.1090/S0025-5718-2011-02535-4zbMath1329.11108MaRDI QIDQ5389444

Djamel Berkane, Olivier Ramaré, Olivier Bordellès

Publication date: 26 April 2012

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

Mathematics Subject Classification ID

Quadratic extensions (11R11) Asymptotic results on arithmetic functions (11N37) Class numbers, class groups, discriminants (11R29) Software, source code, etc. for problems pertaining to number theory (11-04) Rate of growth of arithmetic functions (11N56)

Related Items (9)

Searching for Diophantine quintuples ⋮ Some elementary explicit bounds for two mollifications of the Moebius function ⋮ Explicit estimates on the summatory functions of the Möbius function with coprimality restrictions ⋮ Explicit zero density estimate for the Riemann zeta-function near the critical line ⋮ Improved Bounds on Brun’s Constant ⋮ Two explicit divisor sums ⋮ Explicit estimates on several summatory functions involving the Moebius function ⋮ Bounds on the number of Diophantine quintuples ⋮ Atkinson's formula for the mean square of \(\zeta (s)\) with an explicit error term

Uses Software

• PARI/GP

Cites Work

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• On sums of primes
• Explicit estimates for the Riemann zeta function
• Approximate formulae for L(1,χ)
• An integral involving the remainder term in the Piltz divisor problem
• ON THE MEAN SQUARE OF THE RIEMANN ZETA-FUNCTION
• Sommes de diviseurs et structure multiplicative des entiers
• Upper bounds for class numbers of real quadratic fields
• Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants
• Primes in arithmetic progressions
• Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients

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