Evaluating Prime Power Gauss and Jacobi Sums

2014/10/22 by Misty Long, Long, Misty, Vincent Pigno +3
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1410.6179

openalex publication_date 2014/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any mod p^m characters, χ₁, …, χ_k, the Jacobi sum, ∑_x1=1^pm… ∑_\substackx_k=1
x₁+…+x_k=B^pmχ₁(x₁)… χ_k(x_k), has a simple evaluation when m is sufficiently large (for m≥ 2 if p\nmid B). As part of the proof we give a simple evaluation of the mod p^m Gauss sums when m≥ 2.

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