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ISSN 1088-6850(e) ISSN 0002-9947(p)

Functional equations of -functions for symmetric products of the Kloosterman sheaf

Author(s): Lei Fu; Daqing Wan
Journal: Trans. Amer. Math. Soc. 362 (2010), 5947-5965.
MSC (2000): Primary 11L05, 14G15
Posted: June 14, 2010
MathSciNet review: 2661503
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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 -functions for these symmetric products and prove a conjecture of Evans on signs of constants of functional equations.

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