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Asymptotic variation of L functions of one-variable exponential sums | | Hui June Zhu
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26 Jun 2002 | | Journal: | J. Reine Angew. Math., 572 (2004), 219--233 | | Subject: | Number Theory; Algebraic Geometry | math.NT math.AG | | Abstract: | Let d>2 and let p be a prime coprime to d. Let Z_pbar be the ring of integers of Q_pbar. Suppose f(x) is a degree-d polynomial over Qbar and Z_pbar. Let P be a prime ideal over p in the ring of integers of Q(f), where Q(f) is the number field generated by coefficients of f in Qbar. Let A^d be the dimension-d affine space over Qbar, identified with the space of coefficients of degree-d monic polynomials. Let NP(f mod P) denote the p-adic Newton polygon of L(f mod P;T). Let HP(A^d) denote the p-adic Hodge polygon of A^d. We prove that there is a Zariski dense open subset U defined over Q in A^d such that for every geometric point f(x) in U(Qbar) we have lim_{p-->oo} NP(f mod P) = HP(A^d), where P is any prime ideal in the ring of integers of Q(f) lying over p. This proves a conjecture of Daqing Wan. | | Source: | arXiv, math.NT/0206284 | | Services: | Forum | Review | PDF | Favorites | |
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