Alexandre Benoist

PhD student in number theory at the University of Luxembourg.

Welcome to my webpage ! I am a PhD student in mathematics at the University of Luxembourg, working under the supervision of Antonella Perucca. My interests mainly lie in number theory, and I am currently working on the arithmetic of abelian varieties and isogenies. During the first year of my PhD, I worked on the distribution of Elkies primes for reductions of abelian varieties and on two variants of a conjecture of Lang and Trotter on primitive points for reductions of elliptic curves.

Research

Publications:

  1. with Szabolcs Buzogány and Antonella Perucca. On the independence of divisibility conditions for elliptic curves. Journal of Number Theory, 289 (2026). Journal, Orbilu. Code
  2. with Antonella Perucca. Two natural variants of the Lang-Trotter conjecture on primitive points for elliptic curves. Research in Number Theory, 12 (2026). Journal, Orbilu. Code
  3. with Jean Kieffer. The asymptotic distribution of Elkies primes for reductions of abelian varieties is Gaussian. Research in Number Theory, 11 (2025). Journal, arXiv, Orbilu.
  4. with Antonella Perucca. The ternary cyclotomic polynomials Φ3pq. Involve, a Journal of Mathematics, 19-1 (2026), 51-72. Journal, Orbilu.

Master thesis:

Statistical properties of isogenies between elliptic curves over finite fields, available here, supervised by Jean Kieffer in the CARAMBA team in Nancy.

Talks

  1. The ternary cyclotomic polynomials. PhD Away Days, Nancy. November 19, 2025. Slides.
  2. The distribution of Elkies primes. Journées Arithmétiques 2025, Luxembourg. June 30, 2025. Slides.
  3. Elliptic curves over finite fields and point counting. Luxembourg PhD Seminar, May 19, 2025. Slides.
  4. The distribution of Elkies primes. Journées C2 2025, Pornichet. April 1, 2025. Slides.

Contact

  • Address: Maison du Nombre Campus Belval, 6 avenue de la Fonte, L-4364 ESCH
  • Office number: 04.35.150
  • Email: alexandre.benoist(at)uni.lu