On the distribution of the divisor function and Hecke eigenvalues

DOI10.1007/s11856-016-1290-0zbMath1342.11080arXiv1404.1579OpenAlexW3100529919MaRDI QIDQ2630876

Stephen Lester, Nadav Yesha

Publication date: 22 July 2016

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

Full work available at URL: https://arxiv.org/abs/1404.1579

zbMATH Keywords

arithmetic progressiondivisor functionHecke eigenvalue

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Forms of half-integer weight; nonholomorphic modular forms (11F37) Arithmetic progressions (11B25)

Related Items (7)

Moments of moments of primes in arithmetic progressions ⋮ Squarefrees are Gaussian in short intervals ⋮ Moments of the distribution of k$k$‐free numbers in short intervals and arithmetic progressions ⋮ 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] ⋮ Fourier coefficients of \(\mathrm{GL}(N)\) automorphic forms in arithmetic progressions ⋮ On the variance of sums of divisor functions in short intervals

Cites Work

• On a variance of Hecke eigenvalues in arithmetic progressions
• Fourier coefficients of \(\mathrm{GL}(N)\) automorphic forms in arithmetic progressions
• Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions
• On the divisor function and the Riemann zeta-function in short intervals
• On the variance of sums of divisor functions in short intervals
• The Variance of the Number of Prime Polynomials in Short Intervals and in Residue Classes
• THE AVERAGE VALUE OF DIVISOR SUMS IN ARITHMETIC PROGRESSIONS
• Exponential Sums and Lattice Points III
• The distribution and moments of the error term in the Dirichlet divisor problem
• Summation Formulae for Coefficients of L-functions
• On the Linear Independence of Fractional Powers of Integers
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