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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Functional equations of $L$-functions for symmetric products of the Kloosterman sheaf
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by Lei Fu and Daqing Wan PDF
Trans. Amer. Math. Soc. 362 (2010), 5947-5965 Request permission

Abstract:

We determine the (arithmetic) local monodromy at $0$ and at $\infty$ of the Kloosterman sheaf using local Fourier transformations and Laumon’s stationary phase principle. We then calculate $\epsilon$-factors for symmetric products of the Kloosterman sheaf. Using Laumon’s product formula, we get functional equations of $L$-functions for these symmetric products and prove a conjecture of Evans on signs of constants of functional equations.
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Additional Information
  • Lei Fu
  • Affiliation: Institute of Mathematics, Nankai University, Tianjin, People’s Republic of China
  • Email: leifu@nankai.edu.cn
  • Daqing Wan
  • Affiliation: Department of Mathematics, University of California, Irvine, California 92697
  • MR Author ID: 195077
  • Email: dwan@math.uci.edu
  • Received by editor(s): January 4, 2009
  • Published electronically: June 14, 2010
  • Additional Notes: The research of the first author was supported by the NSFC (10525107).
  • © Copyright 2010 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 5947-5965
  • MSC (2000): Primary 11L05, 14G15
  • DOI: https://doi.org/10.1090/S0002-9947-2010-05172-4
  • MathSciNet review: 2661503