Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the $\ell$-adic valuation of certain Jacobi sums   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 $y^{\ell} = x^{f} + 1$.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an