Lifts of points on curves and exponential sums

2002/02/20 by Régis Blache, Regis Blache, Blache, Regis
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0202206

19 pages, latex2e

openalex publication_date 2002/02/20 · arxiv created 2003/03/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give bounds for exponential sums over curves defined over Galois rings. We first define summation subsets as the images of lifts of points from affine opens of the reduced curve, and we give bounds for the degrees of their coordinate functions. Then we get bounds for exponential sums, extending results of Kumar et al., Winnie Li over the projective line, and Voloch Walker over elliptic and C_ab curves.

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