Exponential Sums Along p-adic Curves
| dc.creator | Zuniga-Galindo, W. A. | |
| dc.date | 2002-07-23 | |
| dc.date.accessioned | 2026-07-07T04:49:48Z | |
| dc.date.available | 2026-07-07T04:49:48Z | |
| dc.description | Let K be a p-adic field, R the valuation ring of K, and P the maximal ideal of R. Let $Y subseteq R^{2}$ be a non-singular closed curve, and Y_{m} its image in R/P^{m} times R/P^{m}, i.e. the reduction modulo P^{m} of Y. We denote by Psi an standard additive character on K. In this paper we discuss the estimation of exponential sums of type S_{m}(z,Psi,Y,g):= $sum\limits_{x in Y_{m}}$ Psi(zg(x)), with z in K, and g a polynomial function on Y. We show that if the p-adic absolute value of z is big enough then the complex absolute value of S_{m}(z,Psi,Y,g) is O(q^{m(1-beta(f,g))}), for a positive constant beta(f,g) satisfying 0<beta(f,g)<1. | |
| dc.description | 9 pages. Accepted in Finite Fields and Their Applications | |
| dc.identifier | https://arxiv.org/abs/math/0207201 | |
| dc.identifier | http://arxiv.org/abs/math/0207201 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64561 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | Primary 11L40, 11T55 | |
| dc.title | Exponential Sums Along p-adic Curves | |
| dc.type | text |