Additive twists of Fourier coefficients of symmetric-square lifts

DOI10.1016/j.jnt.2011.12.017zbMath1319.11025arXiv1106.1456OpenAlexW2076873277MaRDI QIDQ415264

Xiaoqing Li, Matthew P. Young

Publication date: 11 May 2012

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

Full work available at URL: https://arxiv.org/abs/1106.1456

zbMATH Keywords

Fourier coefficientMaass formadditive twistsymmetric-square lift

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Fourier coefficients of automorphic forms (11F30)

Related Items (14)

Asymptotics for cuspidal representations by functoriality from \(\mathrm{GL}(2)\) ⋮ On exponential sums involving Fourier coefficients of cusp forms over primes ⋮ Hybrid subconvexity bounds for \(L \left( \frac{1}{2}, \mathrm{Sym}^2 f \otimes g\right) \) ⋮ On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms ⋮ Nodal domains of Maass forms. I ⋮ The exponential sums related to cusp forms in the level aspect ⋮ On sums involving Fourier coefficients of Maass forms for \(\mathrm{SL}(3,\mathbb Z)\) ⋮ Additive twists of Fourier coefficients of 𝐺𝐿(3) Maass forms ⋮ Additive twists of Fourier coefficients of modular forms ⋮ Exponential sums related to Maass forms ⋮ Resonance of automorphic forms for 𝐺𝐿(3) ⋮ Weight aspect exponential sums for Fourier coefficients of cusp forms ⋮ Sign changes of coefficients of certain Dirichlet series ⋮ Resonances and \(\Omega\)-results for exponential sums related to Maass forms for \(\mathrm{SL}(n, \mathbb{Z})\)

Uses Software

• GL(n)pack

Cites Work

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• Bilinear forms with Kloosterman fractions
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• Second order average estimates on local data of cusp forms
• Sums of Hecke Eigenvalues over Values of Quadratic Polynomials
• On the Holomorphy of Certain Dirichlet Series
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Upper Bounds on L-Functions at the Edge of the Critical Strip
• Cancellation in additively twisted sums on GL(n)
• Automorphic Forms and L-Functions for the GroupGL(n, R)

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