T-adic exponential sums over finite fields

2008/02/19 by Chunlei Liu, Daqing Wan, Liu, Chunlei +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0802.2589

openalex publication_date 2008/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

T-adic exponential sums associated to a Laurent polynomial f are introduced. They interpolate all classical p^m-power order exponential sums associated to f. The Hodge bound for the Newton polygon of L-functions of T-adic exponential sums is established. This bound enables us to determine, for all m, the Newton polygons of L-functions of p^m-power order exponential sums associated to an f which is ordinary for m=1. Deeper properties of L-functions of T-adic exponential sums are also studied. Along the way, new open problems about the T-adic exponential sum itself are discussed.

Citations

• Generic T-adic exponential sums in one variable
• Generic exponential sums associated to Laurent polynomials in one variable

Related

• Generic T-adic exponential sums in one variable
• T-adic exponential sums of polynomials in one variable
• On L-functions of certain exponential sums
• A sup-Hodge bound for exponential sums
• Hodge-Stickelberger polygons for L-functions of exponential sums of P(x^s)