On the ℓ-adic valuation of certain Jacobi sums

2019/10/31 by Vishal Arul, Arul, Vishal
Mathematics · #11L05 #11R18 #11R27 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11L05 #msc:11R18 #msc:11R27

paper · pdf · doi:10.48550/arxiv.1910.14249

18 pages; improved notation, reorganized sections accordingly, clarified a small subtlety with ell=2 case

openalex publication_date 2019/10/31 · arxiv created 2020/05/03 · arxiv updated 2020/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fix distinct primes ℓ and f, a finite field F_q such that q ≡ 1 \pmodℓ f, and a character χ: F_q^× → C^× of exact order ℓ f. We present a new ℓ-adic congruence for the Jacobi sum J(χ^ℓ, χ^f). These Jacobi sums are Frobenius eigenvalues of the curve y^ℓ = x^f + 1.

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