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p-adic variation of L-functions of exponential sums, I | Hui June Zhu
; | Date: |
18 Nov 2001 | Journal: | American Journal of Mathematics 125 (2003), 669-690. | Subject: | Algebraic Geometry; Number Theory | math.AG math.NT | Abstract: | For a polynomial f(x) in (Z_pcap Q)[x] of degree d>2 let L(f mod p;T) be the L-function of the exponential sum of f mod p. Let NP(f mod p) denote the Newton polygon of L(f mod p;T). Let HP(f) denote the Hodge polygon of f, which is the lower convex hull in the real plane of the points (n,n(n+1)/(2d)) for 0leq nleq d-1. We prove that there is a Zariski dense subset U defined over Q in the space A^d of degree-d monic polynomials over Q such that for all f in U(Q) we have lim NP(f mod p) = HP(f) as p approaches infinity. Moreover, we determine the p-adic valuation of every coefficient of L(f mod p;T) for p large enough and f in U(Q). | Source: | arXiv, math.AG/0111194 | Services: | Forum | Review | PDF | Favorites |
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