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- W4205510680 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. Dans cet article, nous obtenons des formules asymptotiques sur les nil-variétés Γ﹨G, où G est un groupe de Lie nilpotent stratifié (ou même gradué) equipé d'un sous groupe Γ co-compact discret. Nous étudions tout particuliérement les formules asymptotiques en relation aux sous-laplaciens provenant naturellement de la structure stratifiée du groupe G, et plus généralement aux opérateurs de Rockland positifs lorsque G est gradué. Nous montrons que les dévelopements asymptotiques sur la diagonale et en temps court des noyaux des multiplicateurs spectraux contiennent seulement un terme non-trivial. Nous étudions aussi les fonctions de zeta associées." @default.
- W4205510680 created "2022-01-25" @default.
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- W4205510680 date "2022-04-01" @default.
- W4205510680 modified "2023-10-03" @default.
- W4205510680 title "Asymptotics and zeta functions on compact nilmanifolds" @default.
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- W4205510680 doi "https://doi.org/10.1016/j.matpur.2021.12.007" @default.
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