Newton polygons for twisted exponential sums and polynomials $P(x^d)$
| dc.creator | Blache, Regis | |
| dc.creator | Ferard, Eric | |
| dc.date | 2007-02-16 | |
| dc.date | 2007-06-18 | |
| dc.date.accessioned | 2026-07-07T08:10:33Z | |
| dc.date.available | 2026-07-07T08:10:33Z | |
| dc.description | We study the $p$-adic absolute value of the roots of the $L$-functions associated to certain twisted character sums, and additive character sums associated to polynomials $P(x^d)$, when $P$ varies among the space of polynomial of fixed degree $e$ over a finite field of characteristic $p$. For sufficiently large $p$, we determine in both cases generic Newton polygons for these $L$-functions, which is a lower bound for the Newton polygons, and the set of polynomials of degree $e$ for which this generic polygon is attained. In the case of twisted sums, we show that the lower polygon defined in \cite{as1} is tight when $p\equiv 1 [de]$, and that it is the actual Newton polygon for any degree $e$ polynomial. | |
| dc.description | The results in this preprint have been strenghened in arXiv:0706.2340; please look at this new preprint | |
| dc.identifier | https://arxiv.org/abs/math/0702502 | |
| dc.identifier | http://arxiv.org/abs/math/0702502 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131855 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G15, 11T23,11L03 | |
| dc.title | Newton polygons for twisted exponential sums and polynomials $P(x^d)$ | |
| dc.type | text |