Related papers: $p$-kernels occurring in an isogeny class of $p$-d…

The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes…

Let $d \ge 3$ be an integer and let $P \in \mathbb{Z}[x]$ be a polynomial of degree $d$ whose Galois group is $S_d$. Let $(a_n)$ be a linearly recuresive sequence of integers which has $P$ as its characteristic polynomial. We prove, under…

Let $A$ be an abelian variety defined over a number field $K$, $E/K$ be an elliptic curve, and $\phi:A\to E^m$ be an isogeny defined over $K$. Let $P\in A(K)$ be such that $\phi(P)=(Q_1,\dots, Q_m)$ with $\text{Rank}_\mathbb{Z}(\langle…

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…

We propose two inductive approaches for determining the cohomology of Deligne-Lusztig varieties in the case of the general linear group

We consider groups where the centers of the irreducible characters form a chain. We obtain two alternate characterizations of these groups, and we obtain some information regarding the structure of these groups. Using our results, we are…

A longstanding conjecture asserts that every non-abelian finite $p$-group $G$ admits a non-inner automorphism of order $p$. The conjecture is valid for finite $p$-groups of class 2. Here, we prove every finite non-abelian $p$-group $G$ of…

Let a and b be non-zero rational numbers that are multiplicatively independent. We study the natural density of the set of primes p for which the subgroup of the multiplicative group of the finite field with p elements generated by (a\mod…

For an important class of arithmetic Dedekind domains O including the ring of integers of not totally complex number fields, we describe explicitly the group of linear characters of SL_2(O). For this, we determine, for arbitrary Dedekind…

In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature and is not the dual of any PDE. We obtain the existence of…

Consider the problem of efficiently evaluating isogenies $\phi: E \to E/H$ of elliptic curves over a finite field $\mathbb{F}_q$, where the kernel $H = \langle G\rangle$ is a cyclic group of odd (prime) order: given $E$, $G$, and a point…

We extend to arbitrary commutative base rings a recent result of Demeneghi that every ideal of an ample groupoid algebra over a field is an intersection of kernels of induced representations from isotropy groups, with a much shorter proof,…

Given two CM elliptic curves over a number field and a natural number $m$, we establish a polynomial lower bound (in terms of $m$) for the number of rational primes $p$ such that the reductions of these elliptic curves modulo a prime above…

Let $C$ be an affine curve over an algebraically closed field $k$ of characteristic $p>0$. Given an embedding problem $(\beta:\Gamma\longrightarrow G, \alpha: \pi^{et}_1(C)\longrightarrow G)$ for $\pi_1^{et}(C)$ where $\beta$ is a…

We discuss the classification of reflection subgroups of finite and affine Weyl groups from the point of view of their root systems. A short case free proof is given of the well known classification of the isomorphism classes of reflection…

Given a prime power $p^d$ with $p$ a prime and $d$ a positive integer, we classify the finite groups $G$ with $p^{2d}$ dividing $|G|$ in which all subgroups of order $p^d$ are complemented and the finite groups $G$ having a normal…

We prove that a profinite group $G$ with positive rank gradient does not satisfy a group law. In the case when $G$ is a pro-$p$ group we show that $G$ contains a nonabelian dense free subgroup.

This paper concerns finite groups of class (at most) two and of odd prime exponent $p$. Such a group is called special if the center lies within its derived group. Every group of class 2 and exponent $p$ can be uniquely expressed as the…

We study a class of elliptic problems with homogeneous Dirichlet boundary condition and a nonlinear reaction term $f$ which is nonlocal depending on the $L^{p}$-norm of the unknown function. The nonlinearity $f$ can make the problem…

Let $G_n$ denote either the group $SO(2n+1, F)$, $Sp(2n, F)$, or $GSpin(2n+1, F)$ over a non-archimedean local field of characteristic different than two. We determine all composition factors of degenerate principal series of $G_n$, using…