Newton polygons for twisted exponential sums and polynomials P(x^d)

2007/02/16 by Régis Blache, Blache, Regis, Éric Férard +1
Computer Science · Mathematics · #11L03 #11T23 #14G15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0702502

openalex publication_date 2007/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \citeas1 is tight when p≡ 1 [de], and that it is the actual Newton polygon for any degree e polynomial.

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