Higher-Power Moments of δ(x ), E(t ) and P(x )
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Publication:5203117
DOI10.1112/plms/s3-65.1.65zbMath0725.11046OpenAlexW2092380042MaRDI QIDQ5203117
Publication date: 1992
Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/plms/s3-65.1.65
asymptotic formulacircle problemerror termmean valuesDirichlet's divisor problemdivisor summean square formula for the Riemann zeta-function
Asymptotic results on arithmetic functions (11N37) Waring's problem and variants (11P05) (zeta (s)) and (L(s, chi)) (11M06)
Related Items (33)
Tong-type identity and the mean square of the error term for an extended Selberg class ⋮ On some mean values for the divisor function and the Riemann zeta-function ⋮ On the mean of the shifted error term in the theory of the Dirichlet divisor problem ⋮ A weighted divisor problem ⋮ On the fourth power moment of the error term for the divisor problem with congruence conditions ⋮ On the error term \(\Delta_{(k,l)}(x)\) ⋮ On hybrid moments of \(\Delta_2 (x)\) and \(\Delta_3 (x)\) ⋮ On the fourth power moment of Fourier coefficients of cusp form ⋮ The Mean Values of the Riemann Zeta-Function on the Critical Line ⋮ The Circle Problem of Gauss and the Divisor Problem of Dirichlet—Still Unsolved ⋮ Sign changes of \(\Delta_{(1)}(x)\) ⋮ The third-power moment of the Riesz mean error term of symmetric square \(L\)-function ⋮ Prime lattice points in ovals ⋮ Moments and oscillations of exponential sums related to cusp forms ⋮ The variance and correlations of the divisor function in \(\mathbb{F}_q[T\), and Hankel matrices] ⋮ On the seventh power moment of Δ(x) ⋮ Higher moments of the error term in the divisor problem ⋮ Mixed $L^{p}(L^{2})$ norms of the lattice point discrepancy ⋮ On higher-power moments of \(\Delta(1)(x)\) ⋮ Sign changes of the error term in Weyl’s law for Heisenberg manifolds ⋮ Moments of the probability density functions of error terms in divisor problems ⋮ On the third and fourth power moments of Fourier coefficients of cusp forms ⋮ On fourth and higher moments of short exponential sums related to cusp forms ⋮ On the Riemann zeta-function and the divisor problem ⋮ On differences of two squares ⋮ Almost periodic functions and hyperbolic counting ⋮ On the mean square formula of the error term in the Dirichlet divisor problem ⋮ On the Dirichlet divisor problem in short intervals ⋮ Circle problem and the spectrum of the Laplace operator on closed 2-manifolds ⋮ On Wigert's type divisor problem ⋮ 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
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