On the $\ell$-adic valuation of certain Jacobi sums
Vishal Arul

TL;DR
This paper derives a new $ ext{ell}$-adic congruence for Jacobi sums associated with certain algebraic curves over finite fields, enhancing understanding of their valuations and Frobenius eigenvalues.
Contribution
It introduces a novel $ ext{ell}$-adic congruence for Jacobi sums linked to specific algebraic curves over finite fields.
Findings
Established a new $ ext{ell}$-adic congruence for Jacobi sums.
Connected Jacobi sums to Frobenius eigenvalues of algebraic curves.
Provided insights into the $ ext{ell}$-adic valuation of these sums.
Abstract
Fix distinct primes and , a finite field such that , and a character of exact order . We present a new -adic congruence for the Jacobi sum . These Jacobi sums are Frobenius eigenvalues of the curve .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Analytic Number Theory Research
