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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

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Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2018, Issue 745


Addendum to “Singular equivariant asymptotics and Weyl’s law”

Pablo Ramacher
  • Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Str., 35032 Marburg, Germany
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Published Online: 2017-02-25 | DOI: https://doi.org/10.1515/crelle-2017-0001


Let M be a closed Riemannian manifold carrying an effective and isometric action of a compact connected Lie group G. We derive a refined remainder estimate in the stationary phase approximation of certain oscillatory integrals on TM×G with singular critical sets that were examined in [7] in order to determine the asymptotic distribution of eigenvalues of an invariant elliptic operator on M. As an immediate consequence, we deduce from this an asymptotic multiplicity formula for families of irreducible representations in L2(M). The improved remainder is used in [4] to prove an equivariant semiclassical Weyl law and a corresponding equivariant quantum ergodicity theorem.


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    B. Küster and P. Ramacher, Quantum ergodicity and symmetry reduction, J. Funct. Anal. (2017), to appear. Web of ScienceGoogle Scholar

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    O. Paniagua-Taobada and P. Ramacher, Equivariant heat asymptotics on spaces of automorphic forms, Trans. Amer. Math. Soc. 368 (2016), no. 5, 3509–3537. Google Scholar

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    P. Ramacher, Singular equivariant asymptotics and the momentum map. Residue formulae in equivariant cohomology, J. Symplectic Geom. 14 (2016), no. 2, 449–539. Web of ScienceCrossrefGoogle Scholar

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About the article

Received: 2015-09-15

Published Online: 2017-02-25

Published in Print: 2018-12-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2018, Issue 745, Pages 281–293, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2017-0001.

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