Didier Lesesvre

Associate Professor
Université de Lille


Arithmetic statistics on automorphic forms deal with understanding the behavior of families of automorphic representations. Those are much better-behaved than isolated representations. The beginning of the story and the aims of arithmetic statistics are nicely described in this survey.

I am interested more widely in analytic number theory methods and object, as well as the use of trace formulas. I am currently exploring new landscapes: multiple Dirichlet series, moments of L-functions, the (classical and automorphic) circle methods, subconvexity results, integral representations of L-functions, general versions of the Arthur trace formula, and also theories of local newforms.

I would like to export the powerful ideas and results of the classical analytic number theory (on general linear groups) to the setting of general reductive groups. I am working on establishing arithmetic statistics for unitary and symplectic groups of low ranks with Ian Petrow, and developping the necessary tools to do so (a theory of local newforms) on the orthogonal groups with Sarah Dijols.

Publications and preprints

  1. Conductor zeta function for the GL(2) universal family
    with F. Brumley and D. Milićević
    submitted for publication (2021)
  2. Subconvexity for twisted GL(3) L-functions
    with E. M. Kıral and C. I. Kuan
    Acta Arithmetica, to appear (2021)
  3. Sums of even ascending powers and the associated program and data (also on GitHub)
    with C. I. Kuan and X. Xiao
    submitted for publication (2020)
  4. Quadratric Twists of central values: number fields case
    with C. I. Kuan
    Quarterly Journal of Mathematics, to appear (2021)
  5. The Volumes of Miyauchi subgroups
    with I. Petrow
    submitted for publication (2019)
  6. Low-lying zeros of L-functions for Quaternion Algebras
    Ann. Institut Fourier, to appear (2020)
  7. Counting and Equidistribution for Quaternion Algebras
    Math. Zeitschrift (2020) 295:129-159
  8. Optimal transportation with an oscillation-type cost: the one-dimensional case
    with P. Pegon and F. Santambrogio
    Set-Valued Var. Anal (2013) 21:541–556

Publications in pedagogy

  1. Pour un enseignement par la recherche. Compte rendu d'un groupe de travail
    Repères IREM (2020) 121:1-32
  2. L'algèbre, ou l'école de la raison
    Repères IREM (2013) 93:5-36




Here are some notes written as complements to some talks I gave: