Kloosterman-Fourier inversion for symmetric matrices

Omer Offen

Bulletin de la Société Mathématique de France (2005)

  • Volume: 133, Issue: 3, page 331-348
  • ISSN: 0037-9484

Abstract

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We formulate a Kloosterman transform on the space of generalized Kloosterman integrals on symmetric matrices, and obtain an inversion formula. The formula is a step towards a fundamental lemma of the Jacquet type. At the same time it hints towards a conjectural relative trace formula identity, associated with the metaplectic correspondence.

How to cite

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Offen, Omer. "Kloosterman-Fourier inversion for symmetric matrices." Bulletin de la Société Mathématique de France 133.3 (2005): 331-348. <http://eudml.org/doc/272444>.

@article{Offen2005,
abstract = {We formulate a Kloosterman transform on the space of generalized Kloosterman integrals on symmetric matrices, and obtain an inversion formula. The formula is a step towards a fundamental lemma of the Jacquet type. At the same time it hints towards a conjectural relative trace formula identity, associated with the metaplectic correspondence.},
author = {Offen, Omer},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Kloosterman integrals; Kloosterman transform; Jacquet’s relative trace formula},
language = {eng},
number = {3},
pages = {331-348},
publisher = {Société mathématique de France},
title = {Kloosterman-Fourier inversion for symmetric matrices},
url = {http://eudml.org/doc/272444},
volume = {133},
year = {2005},
}

TY - JOUR
AU - Offen, Omer
TI - Kloosterman-Fourier inversion for symmetric matrices
JO - Bulletin de la Société Mathématique de France
PY - 2005
PB - Société mathématique de France
VL - 133
IS - 3
SP - 331
EP - 348
AB - We formulate a Kloosterman transform on the space of generalized Kloosterman integrals on symmetric matrices, and obtain an inversion formula. The formula is a step towards a fundamental lemma of the Jacquet type. At the same time it hints towards a conjectural relative trace formula identity, associated with the metaplectic correspondence.
LA - eng
KW - Kloosterman integrals; Kloosterman transform; Jacquet’s relative trace formula
UR - http://eudml.org/doc/272444
ER -

References

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  1. [1] Y. Flicker & D. Kazhdan – « Metaplectic correspondence », 64 (1986), p. 53–110. Zbl0616.10024MR876160
  2. [2] H. Jacquet – « Facteurs de transfert pour les intégrales de Kloosterman », 336 (2003), no. 2, p. 121–124. Zbl1116.11308MR1969564
  3. [3] —, « Smooth transfer of Kloosterman integrals », 120 (2003), no. 1, p. 121–152. Zbl1060.11032MR2010736
  4. [4] —, « Kloosterman identities over a quadratic extension », Ann. Math. (2) 160 (2004), no. 2, p. 755–779. Zbl1071.11026MR2123938
  5. [5] D. Kazhdan & S. Patterson – « Metaplectic forms », 59 (1982), p. 35–142. Zbl0559.10026MR743816
  6. [6] Z. Mao – « A fundamental lemma for metaplectic correspondence », 496 (1998), p. 107–129. Zbl0890.11019MR1605813
  7. [7] A. Weil – « Sur certains groupes d’opérateurs unitaires », 111 (1964), p. 143–211. Zbl0203.03305MR165033

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