Laboratoire Analyse, Géométrie et Applications

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19982026

F_{q}

are as good as linear codes for q at least four

224 citations

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math.NT2025

On the constituents of the mod $p$ cohomology of Shimura curves

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number and $K$ a finite unramified extension of $Q_{p}$ . When $p$ is large enough with respect to $[K : Q_{p}]$ and under mild genericity assumptions…

math.NT2025

The lifting problem for Galois representations

Alexander Merkurjev, Federico Scavia

We solve the lifting problem for Galois representations in every dimension and in every characteristic. That is, we determine all pairs $(n, k)$ , where $n$ is a positive integer and…

math.NT2024★ 1 cited

Permutation polynomials of finite fields of even characteristic from character sums

Ruikai Chen, Sihem Mesnager

In this paper, we investigate permutation polynomials over the finite field $F_{q^{n}}$ with $q = 2^{m}$ , focusing on those in the form $Tr (A x^{q + 1}) + L (x)$ , where $A\in\…

math.NT2023

On a Class of Permutation Rational Functions Involving Trace Maps

Ruikai Chen, Sihem Mesnager

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of per…

math.NT2023★ 2 cited

Permutation Rational Functions over Quadratic Extensions of Finite Fields

Ruikai Chen, Sihem Mesnager

Permutation rational functions over finite fields have attracted much attention in recent years. In this paper, we introduce a class of permutation rational functions over $\mathbb…

math.NT2023

On a Class of Permutation Polynomials and Their Inverses

Ruikai Chen, Sihem Mesnager

We introduce a class of permutation polynomial over $F_{q^{n}}$ that can be written in the form $\frac{L ( x )}{x ^{q + 1}}$ or $\frac{L ( x ^{q + 1} )}{x}$ for some $q$ -linear polynomial…

On the constituents of the mod p cohomology of Shimura curves

The lifting problem for Galois representations

Permutation polynomials of finite fields of even characteristic from character sums

On a Class of Permutation Rational Functions Involving Trace Maps

Permutation Rational Functions over Quadratic Extensions of Finite Fields

On a Class of Permutation Polynomials and Their Inverses

On the constituents of the mod $p$ cohomology of Shimura curves