On the mean square formula of the error term in the Dirichlet divisor problem

DOI10.1017/S0305004108001874zbMath1229.11125OpenAlexW2002085088MaRDI QIDQ3616233

Yuk-Kam Lau, Kai-Man Tsang

Publication date: 24 March 2009

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004108001874

zbMATH Keywords

Riemann zeta-functioncircle problemmean squareDirichlet divisor problem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) (zeta (s)) and (L(s, chi)) (11M06)

Related Items (18)

Tong-type identity and the mean square of the error term for an extended Selberg class ⋮ On the mean of the shifted error term in the theory of the Dirichlet divisor problem ⋮ On hybrid moments of \(\Delta_2 (x)\) and \(\Delta_3 (x)\) ⋮ The Mean Values of the Riemann Zeta-Function on the Critical Line ⋮ On an analogue of the Gauss circle problem for the Heisenberg group ⋮ On some mean value results for the zeta-function and a divisor problem. II. ⋮ Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function ⋮ On a conjecture of Chowla and Walum ⋮ The mean square discrepancy in the divisor problem ⋮ Sign changes of the error term in Weyl’s law for Heisenberg manifolds ⋮ Mean square of the error term in the asymmetric multidimensional divisor problem ⋮ SECOND MOMENTS IN THE GENERALIZED GAUSS CIRCLE PROBLEM ⋮ On the Dirichlet divisor problem in short intervals ⋮ The mean square discrepancy in the circle problem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ The average behaviour of the error term in a new kind of the divisor problem ⋮ On the differences between two kinds of mean value formulas of number-theoretic error terms

Cites Work

• Large values of the error term in the divisor problem
• Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\)
• Moments over short intervals
• Mean square of the remainder term in the Dirichlet divisor problem
• The mean-value of the Riemann zeta function
• ON THE MEAN SQUARE OF THE RIEMANN ZETA-FUNCTION
• The Fourth Power Moment of the Riemann Zeta Function
• Exponential Sums and Lattice Points III
• On the divisor problem: Moments of Δ(x) over short intervals
• Hilbert's Inequality
• Lattice points in a circle: An improved mean-square asymptotics
• Higher-Power Moments of δ(x ), E(t ) and P(x )

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