Double square moments and bounds for resonance sums of cusp forms

DOI10.1016/j.jnt.2022.11.012OpenAlexW4313367696MaRDI QIDQ2681242

Yangbo Ye, Praneel Samanta, Timothy L. Gillespie

Publication date: 7 February 2023

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

Full work available at URL: https://arxiv.org/abs/2209.03856

zbMATH Keywords

holomorphic cusp formPoisson's summation formularesonance sumhypothesis SPetersson's formularesonance barriersquare moment

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Cites Work

• Unnamed Item
• Hyper-Kloosterman sums of different moduli and their applications to automorphic forms for \(\mathrm{SL}_m(\mathbb{Z})\)
• Resonance between automorphic forms and exponential functions
• Computing the Laplace eigenvalue and level of Maass cusp forms
• On certain exponential sums related to \(\text{GL}(3)\) cusp forms
• Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for \(\mathrm{GL}_m(\mathbb Z)\)
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• Spectral square moments of a resonance sum for Maass forms
• La conjecture de Weil. I
• Weyl bound for GL(2) in \(t\)-aspect via a simple delta method
• Bounds toward hypothesis S for cusp forms
• Resonances and \(\Omega\)-results for exponential sums related to Maass forms for \(\mathrm{SL}(n, \mathbb{Z})\)
• Weighted stationary phase of higher orders
• Double first moment for \(L(\frac{1}{2}, \operatorname{Sym}^2 f \times g)\) by applying Petersson's formula twice
• The lattice point problem of many dimensional hyperboloids. III
• Sums of Fourier coefficients of a Maass form for SL3(ℤ) twisted by exponential functions
• Small eigenvalues of Laplacian for $Γ_{0}(N)$
• ASYMPTOTIC VORONOI'S SUMMATION FORMULAS AND THEIR DUALITY FOR SL₃(ℤ)
• Resonance of automorphic forms for 𝐺𝐿(3)
• Low lying zeros of families of \(L\)-functions
• Resonance sums for Rankin-Selberg products of \(\mathrm{SL}_m(\mathbb{Z})\) Maass cusp forms

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