Evaluating Jacquet’s $\mathbf {{\rm GL}(n)}$ Whittaker function

DOI10.1090/S0025-5718-08-02158-3zbMath1208.33008OpenAlexW1503871316MaRDI QIDQ3055130

Kevin A. Broughan

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-08-02158-3

zbMATH Keywords

unbounded domainquadratureWhittaker functionsymbolic evaluationK-Bessel functionJacquet Whittaker function

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Analysis on real and complex Lie groups (22E30) Classical groups (11E57) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (1)

Evaluating Whittaker functions and Maass forms for 𝑆𝐿(3,ℤ)

Uses Software

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• GL(n)pack

Cites Work

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• On explicit integral formulas for \(\text{GL}(n, \mathbb R)\)-Whittaker functions. With an appendix by Daniel Bump, Solomon Friedberg, and Jeffrey Hoffstein
• Poincaré series for GL(n): Fourier expansion, Kloosterman sums, and algebreo-geometric estimates
• Multiple integration over bounded and unbounded regions
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• Archimedean \(L\)-factors on \(\text{GL}(n)\times\text{GL}(n)\) and generalized Barnes integrals
• A remark on Whittaker functions on SL\((n,{\mathbb R})\).
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• On the integration of products of Whittaker functions with respect to the second index
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• Fonctions de Whittaker associées aux groupes de Chevalley

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