On a variance of Hecke eigenvalues in arithmetic progressions

DOI10.1016/j.jnt.2011.12.011zbMath1287.11058OpenAlexW2099749331MaRDI QIDQ412106

Yuk-Kam Lau, Li Lu Zhao

Publication date: 4 May 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.12.011

zbMATH Keywords

Hecke eigenvaluesBarban-Davenport-Halberstam type theorems

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Hecke-Petersson operators, differential operators (one variable) (11F25) Rate of growth of arithmetic functions (11N56)

Related Items (14)

Sums of divisor functions and von Mangoldt convolutions in \(\mathbb{F}_q [T\) leading to symplectic distributions] ⋮ Higher-power moments of Fourier coefficients of holomorphic cusp forms for the congruence subgroup \(\varGamma_0(N)\) ⋮ On the distribution of the divisor function and Hecke eigenvalues ⋮ Moments of moments of primes in arithmetic progressions ⋮ Divisor problem in arithmetic progressions modulo a prime power ⋮ Variance of sums in arithmetic progressions of divisor functions associated with higher degree L-functions in 𝔽q[t] ⋮ A generalization of the Montgomery-Hooley theorem ⋮ An analogue of the Bombieri-Vinogradov theorem for Fourier coefficients of cusp forms ⋮ Sums of divisor functions in \(\mathbb {F}_q[t\) and matrix integrals] ⋮ Power moments of Hecke eigenvalues for congruence group ⋮ Sign of Fourier coefficients of half-integral weight modular forms in arithmetic progressions ⋮ Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions ⋮ The variance of divisor sums in arithmetic progressions ⋮ A variance for \(k\)-free numbers in arithmetic progressions of given modulus

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