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

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


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

, which we call the Kloosterman sheaf. Let Lp(Gm, Fp, SymkKln+1, s) be the L-function of the k-fold symmetric product of Kln+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 Lp(Gm, Fp, SymkKln+1, s). We also prove similar results for ⊗kKln+1and k Kln+1. © 2008 Springer-Verlag.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View