%0 Journal Article
%T Functional Equations of $L$-Functions for Symmetric Products of the Kloosterman Sheaf
%A Lei Fu
%A Daqing Wan
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0812.4994v1