Asymptotic variation of L functions of one-variable exponential sums
| dc.creator | Zhu, Hui June | |
| dc.date | 2002-06-26 | |
| dc.date | 2005-02-01 | |
| dc.date.accessioned | 2026-07-07T04:49:24Z | |
| dc.date.available | 2026-07-07T04:49:24Z | |
| dc.description | 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. | |
| dc.description | 12 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0206284 | |
| dc.identifier | http://arxiv.org/abs/math/0206284 | |
| dc.identifier | J. Reine Angew. Math., 572 (2004), 219--233 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64409 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Asymptotic variation of L functions of one-variable exponential sums | |
| dc.type | text |