Smooth transfer of Kloosterman integrals

DOI10.1215/S0012-7094-03-12015-3zbMath1060.11032OpenAlexW2104058919MaRDI QIDQ5907050

Hervé Jacquet

Publication date: 28 January 2004

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-03-12015-3

zbMATH Keywords

relative trace formulabase changeKloosterman integral

Mathematics Subject Classification ID

Gauss and Kloosterman sums; generalizations (11L05) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (13)

Holomorphy of adjoint L-functions for \(\mathrm{GL}(n):n\le 4\) ⋮ Kloosterman-Fourier inversion for symmetric matrices ⋮ On the smooth transfer for Guo–Jacquet relative trace formulae ⋮ Supercuspidal representations of \(\mathrm{GL}_n(F)\) distinguished by an orthogonal involution ⋮ Distinction by the quasi-split unitary group ⋮ Spherical varieties, functoriality, and quantization ⋮ Bessel functions and Kloosterman integrals on \(\mathrm{GL}(n)\) ⋮ Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices ⋮ On representations distinguished by unitary groups ⋮ Relative functoriality and functional equations via trace formulas ⋮ Transfer operators and Hankel transforms between relative trace formulas. I: Character theory ⋮ Transfer operators and Hankel transforms between relative trace formulas. II: Rankin-Selberg theory ⋮ Transfer factors for Kloosterman integrals

Cites Work

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• Poincaré series on \(\mathrm{GL}(r)\) and Kloosterman sums
• An integral transform and its applications
• Periods of Eisenstein series: the Galois case
• A theorem of density for Kloosterman integrals
• The continuous spectrum of the relative trace formula for \(GL(3)\) over a quadratic extension
• The fundamental lemma of Jacquet and Ye in positive characteristic
• Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de jacquet et ye
• Relative Kloosterman integrals for GL(3)
• Germs of Kloosterman Integrals for $GL(3)$
• Distinguished representations and quadratic base change for 𝐺𝐿(3)

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