Skip to main content
eScholarship
Open Access Publications from the University of California

UC Irvine

UC Irvine Previously Published Works bannerUC Irvine

L-functions of symmetric products of the Kloosterman sheaf over Z

  • Author(s): Fu, L;
  • Wan, D
  • et al.
Abstract

The classical n-variable Kloosterman sums over the finite field F p give rise to a lisse Q̄l-sheaf Kl n+1 on Gm, Fp}=P1Fp-

, which we call the Kloosterman sheaf. Let L p (G m, Fp , Sym k Kl n+1, s) be the L-function of the k-fold symmetric product of Kl n+1. We construct an explicit virtual scheme X of finite type over Spec Z such that the p-Euler factor of the zeta function of X coincides with L p (G m, Fp , Sym k Kl n+1, s). We also prove similar results for ⊗k Kln+1 and k Kln+1. © 2008 Springer-Verlag.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View