Sum of the Fourier coefficients of \(SL(3, \mathbb{Z})\) Hecke Maass forms over quadratics

DOI10.1016/j.jnt.2023.01.011OpenAlexW4322724569MaRDI QIDQ2696063

Saurabh Kumar Singh, Himanshi Chanana

Publication date: 6 April 2023

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2023.01.011

zbMATH Keywords

Maass formsPoisson summation formulaHecke eigenformsVoronoi summation formula

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Arithmetic functions; related numbers; inversion formulas (11A25)

Uses Software

• GL(n)pack

Cites Work

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• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• Automorphic distributions, \(L\)-functions, and Voronoi summation for \(\text{GL}(3)\)
• Spectral decompositions of certain automorphic functions and their number-theoretic applications
• Upper and lower bounds at \(s=1\) for certain Dirichlet series with Euler product.
• A twist of the Gauss circle problem by holomorphic cusp forms
• On the number of divisors of quadratic polynomials
• A polynomial divisor problem
• Sums of Hecke Eigenvalues over Values of Quadratic Polynomials
• Exponential Sums and Lattice Points
• A new form of the circle method, and its application to quadratic forms.
• Summation Formulae for Coefficients of L-functions
• Cancellation in additively twisted sums on GL(n)
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• On the Sum ∑k=1xd(f(k))

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