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Functional equations of L-functions for symmetric products of the kloosterman sheaf

Abstract

We determine the (arithmetic) local monodromy at 0 and at ∞ of the Kloosterman sheaf using local Fourier transformations and Laumon's stationary phase principle. We then calculate ε-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. © 2010 American Mathematical Society.

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