Exponential Sums Along p-adic Curves

dc.creatorZuniga-Galindo, W. A.
dc.date2002-07-23
dc.date.accessioned2026-07-07T04:49:48Z
dc.date.available2026-07-07T04:49:48Z
dc.descriptionLet 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.description9 pages. Accepted in Finite Fields and Their Applications
dc.identifierhttps://arxiv.org/abs/math/0207201
dc.identifierhttp://arxiv.org/abs/math/0207201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64561
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subjectPrimary 11L40, 11T55
dc.titleExponential Sums Along p-adic Curves
dc.typetext

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