- Adic Variation of L Functions of Exponential Sums
نویسنده
چکیده
For a polynomial f(x) in (Zp∩Q)[x] of degree d ≥ 3 let L(f⊗Fp;T ) be the L function of the exponential sum of f mod p. Let NP(f ⊗ Fp) denote the Newton polygon of L(f⊗Fp; T ). Let HP(f) denote the Hodge polygon of f , which is the lower convex hull in R2 of the points (n, n(n+1) 2d ) for 0 ≤ n ≤ d−1. We prove that there is a Zariski dense subset U defined over Q in the space A of degree-d monic polynomials over Q such that limp→∞ NP(f ⊗Fp) = HP(f) for all f ∈ U(Q). Moreover, we determine the p-adic valuation of every coefficient of L(f ⊗ Fp;T ) for p large enough and f in U(Q).
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