Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

DOI10.4171/CMH/342zbMath1306.11079arXiv1301.0214MaRDI QIDQ484267

Étienne Fouvry, Philippe Michel, Satadal Ganguly, Emmanuel Kowalski

Publication date: 6 January 2015

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.0214

zbMATH Keywords

monodromy groupcentral limit theoremKloosterman sumsdivisor functionarithmetic progressionsHecke eigenvaluesFourier coefficients of modular formsSato-Tate equidistribution

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Asymptotic results on arithmetic functions (11N37) Exponential sums (11T23) Gauss and Kloosterman sums; generalizations (11L05) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Related Items (22)

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 ⋮ Bilinear forms with Kloosterman sums and applications ⋮ Gaussian distributions of Kloosterman sums: vertical and horizontal ⋮ Kloosterman sums and a problem of D. H. Lehmer ⋮ Moments of moments of primes in arithmetic progressions ⋮ Ultra-short sums of trace functions ⋮ Bilinear forms with trace functions over arbitrary sets and applications to Sato-Tate ⋮ Moments of the distribution of k$k$‐free numbers in short intervals and arithmetic progressions ⋮ Sums of divisor functions in \(\mathbb {F}_q[t\) and matrix integrals] ⋮ Power moments of Hecke eigenvalues for congruence group ⋮ Counting integer points on quadrics with arithmetic weights ⋮ Sign of Fourier coefficients of half-integral weight modular forms in arithmetic progressions ⋮ Fourier coefficients of \(\mathrm{GL}(N)\) automorphic forms in arithmetic progressions ⋮ The variance of divisor sums in arithmetic progressions ⋮ Squarefree Integers in Arithmetic Progressions to Smooth Moduli ⋮ On Bourgain's bound for short exponential sums and squarefree numbers ⋮ On superorthogonality ⋮ Nonvanishing of Dirichlet \(L\)-functions. II ⋮ A lower bound for the variance of generalized divisor functions in arithmetic progressions ⋮ Fourier transforms of hyperbolic invariance functions on \(\mathbb{R}^2\) ⋮ Squarefree numbers in arithmetic progressions

Cites Work

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• Bessel identities in the Waldspurger correspondence over the real numbers
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• THE AVERAGE VALUE OF DIVISOR SUMS IN ARITHMETIC PROGRESSIONS
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Exponential Sums and Differential Equations. (AM-124)
• On the pseudorandomness of the signs of Kloosterman sums
• On the distribution of the divisor function in arithmetic progressions
• Primes in arithmetic progressions
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