Asymptotics and zeta functions on compact nilmanifolds

Research output: Contribution to journalArticlepeer-review

1 Citation (SciVal)

Abstract

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
Volume160
Early online date4 Mar 2022
DOIs
Publication statusPublished - 30 Apr 2022

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Asymptotics and zeta functions on compact nilmanifolds'. Together they form a unique fingerprint.

Cite this