Hodge-Stickelberger polygons for L-functions of exponential sums of P(x^s)
| dc.creator | Blache, Regis | |
| dc.creator | Ferard, Eric | |
| dc.creator | Zhu, Hui June | |
| dc.date | 2007-06-15 | |
| dc.date | 2007-09-20 | |
| dc.date.accessioned | 2026-07-07T08:30:43Z | |
| dc.date.available | 2026-07-07T08:30:43Z | |
| dc.description | Let P(x) be a one-variable Laurent polynomial of degree (d_1,d_2) over a finite field of characteristic p. For any fixed positive integer s not divisible by p, we prove that the (normalized) p-adic Newton polygon of the L-functions of exponential sums of P(x^s) has a tight lower bound which we call `Hodge-Stickelberger polygon', depending only on d_1,d_2,s, and (p mod s). This Hodge-Stickelberger polygon is a weighted convolution of a `Hodge polygon' for L-function of exponential sum of P(x) and the `Newton polygon' for L-function of exponential sum of x^s (given by the classical Stickelberger theory). We prove an analogous Hodge-Stickelberger lower bound for multivariable Laurent polynomials as well. We prove this Hodge-Stickelberger polygon is the limit of generic Newton polygons of P(x^s) in a sense that was made explicit in the paper. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/0706.2340 | |
| dc.identifier | http://arxiv.org/abs/0706.2340 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138307 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11,14 | |
| dc.title | Hodge-Stickelberger polygons for L-functions of exponential sums of P(x^s) | |
| dc.type | text |