Asymptotics for cuspidal representations by functoriality from \(\mathrm{GL}(2)\)

DOI10.1016/J.JNT.2016.01.008zbMath1416.11069arXiv1510.01208OpenAlexW2963392630MaRDI QIDQ266622

Huixue Lao, Mark McKee, Yangbo Ye

Publication date: 13 April 2016

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

Full work available at URL: https://arxiv.org/abs/1510.01208

zbMATH Keywords

asymptotic expansionFourier coefficientcuspidal representationfunctoriality\(\mathrm{GL}(2)\)

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (6)

Sign changes and nonvanishing of Fourier coefficients of holomorphic cusp forms ⋮ Some density results on sets of primes for Hecke eigenvalues ⋮ Power moments of automorphic \(L\)-functions related to Maass forms for \(\mathrm{SL}_3 (\mathbb{Z})\) ⋮ The third-power moment of the Riesz mean error term of symmetric square \(L\)-function ⋮ Integral power sums of Fourier coefficients of symmetric square $L$-functions ⋮ Dirichlet series, asymptotics, and statistics based on functoriality from GL(2)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Additive twists of Fourier coefficients of symmetric-square lifts
• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• The sixth and eighth moments of Fourier coefficients of cusp forms
• Integral mean square estimation for the error term related to \(\sum_{n\leq x}\lambda ^2 (n^2)\)
• On an open problem of Sankaranarayanan
• On the estimation of eigenvalues of Hecke operators
• Modularity of the Rankin-Selberg \(L\)-series, and multiplicity one for \(\mathrm{SL}(2)\)
• La conjecture de Weil. I
• Cuspidality of symmetric powers with applications.
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• Lectures on automorphic \(L\)-functions
• Zeros of principal \(L\)-functions and random matrix theory
• Decoupling, exponential sums and the Riemann zeta function
• On Higher Moments of Fourier Coefficients of Holomorphic Cusp Forms
• A Cuspidality Criterion for the Exterior Square Transfer of Cusp Forms on GL(4)
• Integral power sums of Hecke eigenvalues
• SUMS OF FOURIER COEFFICIENTS OF CUSP FORMS
• Le spectre résiduel de ${\rm GL}(n)$
• On Euler Products and the Classification of Automorphic Representations I
• 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
• The average behavior of Fourier coefficients of cusp forms over sparse sequences
• The distribution of Fourier coefficients of cusp forms over sparse sequences

This page was built for publication: Asymptotics for cuspidal representations by functoriality from \(\mathrm{GL}(2)\)