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

Vishal Arul

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arXiv · 1910.14249

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

Vishal Arul

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Abstract

Fix distinct primes $\ell$ and $f$, a finite field $\mathbf{F}_{q}$ such that $q \equiv 1 \pmod{\ell f}$, and a character $\chi : \mathbf{F}_{q}^{\times} \to \mathbf{C}^{\times}$ of exact order $\ell f$. We present a new $\ell$-adic congruence for the Jacobi sum $J(\chi^{\ell}, \chi^{f})$. These Jacobi sums are Frobenius eigenvalues of the curve $y^{\ell} = x^{f} + 1$.

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Vishal Arul. 2019-10-31. On the $\ell$-adic valuation of certain Jacobi sums. https://arxiv.org/abs/1910.14249

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