Asymptotics and zeta functions on compact nilmanifolds

Véronique Fischer

doi:10.1016/j.matpur.2021.12.007

Asymptotics and zeta functions on compact nilmanifolds

Véronique Fischer

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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 language	English
Pages (from-to)	1-28
Number of pages	28
Journal	Journal des Mathematiques Pures et Appliquees
Volume	160
Early online date	4 Mar 2022
DOIs	https://doi.org/10.1016/j.matpur.2021.12.007
Publication status	Published - 30 Apr 2022

Bibliographical note

Funding Information:
This work is supported by the Leverhulme Trust , Research Project Grant 2020-037.

Keywords

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

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1016/j.matpur.2021.12.007

JMPApaper.PDFAccepted author manuscript, 375 KBLicence: CC BY-NC-ND

https://arxiv.org/pdf/2112.01246.pdfLicence: CC BY
https://arxiv.org/abs/2112.01246Licence: CC BY

Cite this

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title = "Asymptotics and zeta functions on compact nilmanifolds",

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.",

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Y1 - 2022/4/30

N2 - 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.

AB - 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.

KW - Global analysis and spectral problems

KW - Harmonic analysis on homogeneous spaces

KW - Heat kernels

KW - Hypoelliptic operators

KW - Spectral multipliers

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JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Asymptotics and zeta functions on compact nilmanifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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