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  • [hal-01618616] A bound on the primes of bad reduction for CM curves of genus 3

    18 octobre, par Pınar Kılıçer, Kristin Lauter, Elisa Lorenzo García, Rachel Newton, Ekin Ozman
    We give bounds on the primes of geometric bad reduction for curves of genus three of primitive CM type in terms of the CM orders. In the case of genus one, there are no primes of geometric bad reduction because CM elliptic curves are CM abelian varieties, which have potential good reduction (...)
  • [hal-01174473] Principe de Mazur pour U(1,d)

    17 octobre, par Pascal Boyer
    Le principe de Mazur fournit des conditions simples pour qu'une F l-représentation irréductible non ramifiée provenant d'une forme modulaire de niveau Γ 0 (N p) provienne aussi d'une forme de niveau Γ 0 (N). L'objectif de ce travail est de proposer une généralisation de ce principe en dimension (...)
  • [hal-01614087] A common approach to Brocard’s problem, the problem of the infinitude of primes of the form n^2+1, and the twin prime problem

    16 octobre, par Apoloniusz Tyszka
    Let f(3)=4, and let f(n+1)=f(n)! for every integer n \geq 3. For an integer n \geq 3, let \Phi_n denote the following statement: if a system S \subseteq x_i!=x_i+1: 1 \leq i \leq n-1 \cup x_i \cdot x_j=x_j+1: 1 \leq i \leq j \leq n-1 has at most finitely many solutions in integers x_1,...,x_n (...)
  • [hal-00806518] The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups

    16 octobre, par Christophe Delaunay, Frédéric Jouhet
    This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result due to E. Fouvry and J. Klüners which proves that a (...)
  • [hal-00868110] Conditional expanding bounds for two-variables functions over prime fields

    16 octobre, par Norbert Hegyvári, François Hennecart
    In this paper we provide in $\bFp$ expanding lower bounds for two variables functions $f(x,y)$ in connection with the product set or the sumset. The sum-product problem has been hugely studied in the recent past. A typical result in $\bFp^*$ is the existenceness of $\Delta(\alpha)>0$ such (...)

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