L-functions of Symmetric Products of the Kloosterman Sheaf over Z
نویسندگان
چکیده
The classical n-variable Kloosterman sums over the finite field Fp give rise to a lisse Ql-sheaf Kln+1 on Gm,Fp = P 1 Fp − {0,∞}, which we call the Kloosterman sheaf. Let Lp(Gm,Fp ,Sym Kln+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 ,Sym Kln+1, s). We also prove similar results for ⊗Kln+1 and ∧k Kln+1.
منابع مشابه
Functional Equations of L-functions for Symmetric Products of the Kloosterman Sheaf
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