On the mean of the shifted error term in the theory of the Dirichlet divisor problem

DOI10.1216/RMJ-2016-46-1-105zbMath1344.11058OpenAlexW2398491627MaRDI QIDQ289703

Xiaodong Cao, Jun Furuya, Yoshio Tanigawa, Zhai, Wenguang

Publication date: 31 May 2016

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1464035854

zbMATH Keywords

Bernoulli polynomialDirichlet divisor problemmean value formulas

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) (zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Cites Work

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• On the average orders of the error term in the Dirichlet divisor problem
• On the mean square of the error term for the asymmetric two-dimensional divisor problems. II
• Dirichlet series obtained from the error term in the Dirichlet divisor problem
• Mean square of the remainder term in the Dirichlet divisor problem
• On the higher moments of the error term in the divisor problem
• On the differences between two kinds of mean value formulas of number-theoretic error terms
• On the mean square formula of the error term in the Dirichlet divisor problem
• An integral involving the remainder term in the Piltz divisor problem
• Exponential Sums and Lattice Points III
• On higher-power moments of Δ(x) (II)
• Higher-Power Moments of δ(x ), E(t ) and P(x )
• On higher-power moments of Δ(x) (III)

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