Functional equations of L-functions for symmetric products of the kloosterman sheaf
- Author(s): Fu, L
- Wan, D
- et al.
Published Web Locationhttps://doi.org/10.1090/S0002-9947-2010-05172-4
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.