On the variance of sums of divisor functions in short intervals

DOI10.1090/proc/12914zbMath1352.11091arXiv1502.01170OpenAlexW2963524379MaRDI QIDQ2827352

Stephen Lester

Publication date: 19 October 2016

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

Full work available at URL: https://arxiv.org/abs/1502.01170

zbMATH Keywords

Lindelöf hypothesis\(k\)-fold divisor functionvariance of sums

Mathematics Subject Classification ID

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

Related Items (10)

Sums of divisor functions and von Mangoldt convolutions in \(\mathbb{F}_q [T\) leading to symplectic distributions] ⋮ On the distribution of the divisor function and Hecke eigenvalues ⋮ Variance of the $k$-fold divisor function in arithmetic progressions for individual modulus ⋮ The variance and correlations of the divisor function in \(\mathbb{F}_q[T\), and Hankel matrices] ⋮ Sums of divisor functions in \(\mathbb {F}_q[t\) and matrix integrals] ⋮ On short sums involving Fourier coefficients of Maass forms ⋮ The variance of divisor sums in arithmetic progressions ⋮ Some multidimensional integrals in number theory and connections with the Painlevé V equation ⋮ On the mean square of an arithmetical error term of the Selberg class in short intervals ⋮ The variance of the number of sums of two squares in [inline-graphic 01 [T] in short intervals]

Cites Work

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• Moments of the Riemann zeta function
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• On the divisor function and the Riemann zeta-function in short intervals
• Sums of divisor functions in \(\mathbb {F}_q[t\) and matrix integrals]
• Moments of products of automorphic \(L\)-functions
• On the distribution of the divisor function and Hecke eigenvalues
• On the symmetry of the divisor function in almost all short intervals
• The distribution and moments of the error term in the Dirichlet divisor problem
• Summation Formulae for Coefficients of L-functions

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