Exponential sums for \(GL(n)\) and their applications to base change

DOI10.1006/JNTH.1997.2196zbMath0922.11066OpenAlexW2091481400MaRDI QIDQ1385268

Yangbo Ye

Publication date: 3 October 1999

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

Full work available at URL: https://doi.org/10.1006/jnth.1997.2196

zbMATH Keywords

Weyl groupexponential sumsKloosterman sumrelative trace formulabase changeautomorphic representationsShalika germ

Mathematics Subject Classification ID

Gauss and Kloosterman sums; generalizations (11L05) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (1)

A hyper-Kloosterman sum identity

Cites Work

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• Poincaré series on \(\mathrm{GL}(r)\) and Kloosterman sums
• Modular forms associated to real quadratic fields
• A trace formula for dual pairs
• The lifting of Kloosterman sums
• Poincaré series and Kloosterman sums for SL(3, Z)
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
• Relative Kloosterman integrals for GL(3)
• The lifting of an exponential sum to a cyclic algebraic number field of prime degree
• Germs of Kloosterman Integrals for $GL(3)$
• Distinguished representations and quadratic base change for 𝐺𝐿(3)

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