An orthogonality relation for (with an appendix by Bingrong Huang)

DOI10.1017/fms.2021.39zbMath1478.11078arXiv1910.13586OpenAlexW3169710091MaRDI QIDQ4992411

Michael Woodbury, Eric Stade, Dorian Goldfeld

Publication date: 8 June 2021

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.13586

zbMATH Keywords

orthogonality relationKuznetsov trace formula

Mathematics Subject Classification ID

Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (4)

On signs of Fourier coefficients of Hecke-Maass cusp forms on 𝐺𝐿₃ ⋮ The cubic Pell equation $L$-function ⋮ The Relative Trace Formula in Analytic Number Theory ⋮ Applications of analytic newvectors for \(\operatorname{GL}(N)\)

Uses Software

• GL(n)pack

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Sato-Tate law for \(\mathrm{GL}(3)\)
• Weighted Sato-Tate vertical distribution of the Satake parameter of Maass forms on \(\mathrm{PGL}(N)\)
• Poincaré series on \(\mathrm{GL}(r)\) and Kloosterman sums
• Poincaré series for GL(n): Fourier expansion, Kloosterman sums, and algebreo-geometric estimates
• On the functional equations satisfied by Eisenstein series
• Fourier coefficients of cusp forms
• Gelfand-Kirillov dimension for Harish-Chandra modules
• Kloosterman sets in reductive groups
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• Archimedean \(L\)-factors on \(\text{GL}(n)\times\text{GL}(n)\) and generalized Barnes integrals
• The highest lowest zero and other applications of positivity
• A new method for lower bounds of \(L\)-functions
• Mellin transforms of Whittaker functions on \(\text{GL} (4,\mathbb{R})\) and \(\text{GL} (4,\mathbb{C})\)
• Recurrence relations for Mellin transforms of \(G L(n, \mathbb{R})\) Whittaker functions
• Standard zero-free regions for Rankin-Selberg \(L\)-functions via sieve theory
• Supnorm of an eigenfunction of finitely many Hecke operators
• Applications of the Kuznetsov formula on \(\mathrm{GL}(3)\)
• Sato-Tate theorem for families and low-lying zeros of automorphic \(L\)-functions. Appendix A by Robert Kottwitz, and Appendix B by Raf Cluckers, Julia Gordon and Immanuel Halupczok.
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• On the determination of the Plancherel measure for Lebedev–Whittaker transforms on \mathop GL(n)
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• The Residual Spectrum ofG₂
• The distribution of the eigenvalues of Hecke operators
• An orthogonality relation for a thin family of GL(3) Maass forms
• Analytic Proof of the Strong Multiplicity One Theorem
• A stationary phase formula for exponential sums over $ℤ/p^{m}ℤ$ and applications to GL(3)-Kloosterman sums
• Plancherel Distribution of Satake Parameters of Maass Cusp Forms on GL3
• A Standard Zero Free Region for Rankin–Selberg L-Functions
• Mellin transforms of Whittaker functions
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• On the GL(3) Kuznetsov Formula with applications to Symmetry Types of families of $L$-functions
• Fonctions de Whittaker associées aux groupes de Chevalley
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
• On Some Exponential Sums

This page was built for publication: An orthogonality relation for (with an appendix by Bingrong Huang)