Asymptotics and zeta functions on compact nilmanifolds

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In this paper, we obtain asymptotic formulae on nilmanifolds Γ﹨G, where G is any stratified (or even graded) nilpotent Lie group equipped with a co-compact discrete subgroup Γ. We study especially the asymptotics related to the sub-Laplacians naturally coming from the stratified structure of the group G (and more generally any positive Rockland operators when G is graded). We show that the short-time asymptotic on the diagonal of the kernels of spectral multipliers contains only a single non-trivial term. We also study the associated zeta functions.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalJournal des Mathematiques Pures et Appliquees
Early online date4 Mar 2022
Publication statusPublished - 30 Apr 2022


  • Global analysis and spectral problems
  • Harmonic analysis on homogeneous spaces
  • Heat kernels
  • Hypoelliptic operators
  • Spectral multipliers

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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