Duke Mathematical Journal

Smooth transfer of Kloosterman integrals

Hervé Jacquet

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Abstract

We establish the existence of smooth transfer between absolute Kloosterman integrals and Kloosterman integrals relative to a quadratic extension.

Article information

Source
Duke Math. J., Volume 120, Number 1 (2003), 121-152.

Dates
First available in Project Euclid: 16 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1082138627

Digital Object Identifier
doi:10.1215/S0012-7094-03-12015-3

Mathematical Reviews number (MathSciNet)
MR2010736

Zentralblatt MATH identifier
1060.11032

Subjects
Primary: 11F72: Spectral theory; Selberg trace formula 11L05: Gauss and Kloosterman sums; generalizations

Citation

Jacquet, Hervé. Smooth transfer of Kloosterman integrals. Duke Math. J. 120 (2003), no. 1, 121--152. doi:10.1215/S0012-7094-03-12015-3. https://projecteuclid.org/euclid.dmj/1082138627


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References

  • D. Bump, S. Friedberg, and D. Goldfeld, ``Poincaré series and Kloosterman sums'' in The Selberg Trace Formula and Related Topics (Brunswick, Maine, 1984), Contemp. Math. 53, Amer. Math. Soc., Providence, 1986, 39--49.
  • H. Jacquet, The continuous spectrum of the relative trace formula for $\GL(3)$ over a quadratic extension, Israel J. Math. 89 (1995), 1--59.
  • --. --. --. --., A theorem of density for Kloosterman integrals, Asian J. Math. 2 (1998), 759--778.
  • H. Jacquet and Y. Ye, Relative Kloosterman integrals for $\GL(3)$, Bull. Soc. Math. France 120 (1992), 263--295.
  • --. --. --. --., Distinguished representations and quadratic base change for $\GL(3)$, Trans. Amer. Math. Soc. 348 (1996), 913--939.
  • --. --. --. --., Germs of Kloosterman integrals for $\GL(3)$, Trans. Amer. Math. Soc. 351 (1999), 1227--1255.
  • --------, Kloosterman integrals over a quadratic extension, to appear in Ann. of Math. (2).
  • E. Lapid and J. Rogawski, Periods of Eisenstein series: The Galois case, Duke Math. J. 120 (2003), 153--226.
  • B. C. Ngô, Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de Jacquet et Ye, Ann. Sci. École Norm. Sup. (4) 32 (1999), 619--679.
  • --. --. --. --., Le lemme fondamental de Jacquet et Ye en caractéristique positive, Duke Math. J. 96 (1999), 473--520.
  • T. A. Springer, ``Some results on algebraic groups with involutions'' in Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983), Adv. Stud. Pure Math. 6, North-Holland, Amsterdam, 1985, 525--543.
  • G. Stevens, Poincaré series on $\GL(r)$ and Kloostermann sums, Math. Ann. 277 (1987), 25--51.
  • J. L. Waldspurger, Le lemme fondamental implique le transfert, Compositio Math. 105 (1997), 153--236.
  • Y. Ye, The fundamental lemma of a relative trace formula for $\GL(3)$, Compositio Math. 89 (1993), 121--162.
  • --. --. --. --., An integral transform and its applications, Math. Ann. 30 (1994), 405--417.