Functional Equations of L-Functions for Symmetric Products of the Kloosterman Sheaf

2008/12/30 by Lei Fu, Daqing Wan, Fu, Lei +1
Mathematics · #11L05 #14G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11L05 #msc:14G15

paper · pdf · doi:10.48550/arxiv.0812.4994

23 pages

arxiv created 2008/12/30 · arxiv updated 2009/12/01

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.

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