Finite monodromy of some two-parameter families of exponential sums

2024/06/14 by Francisco García-Cortés, García-Cortés, Francisco, Antonio Rojas‐León +1 · 1 citation
Mathematics · #11L05 #11L73 #Algebraic Geometry (math.AG) #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2406.10385

openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We determine the set of polynomials f(x)∈ k[x], where k is a finite field, such that the local system on \mathbb G_m² which parametrizes the family of exponential sums (s,t)↦∑_{x∈ k}ψ(sf(x)+tx) has finite monodromy, in two cases: when f(x)=x^d+λx^e is a binomial and when f(x)=(x-α)^d(x-β)^e is of Belyi type.

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• Gauss--Heilbronn Sums and Coverings of Deligne--Lusztig Type Curves

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