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dc.contributor.author
Lauret, Emilio Agustin
dc.contributor.author
Miatello, Roberto Jorge
dc.contributor.author
Rossetti, Juan Pablo
dc.date.available
2022-09-08T14:54:55Z
dc.date.issued
2021-06
dc.identifier.citation
Lauret, Emilio Agustin; Miatello, Roberto Jorge; Rossetti, Juan Pablo; Recent results on the spectra of lens spaces; Springer; São Paulo Journal of Mathematical Sciences; 15; 6-2021; 240-267
dc.identifier.issn
1982-6907
dc.identifier.uri
http://hdl.handle.net/11336/167969
dc.description.abstract
In this paper we report on recent results by several authors, on the spectral theory of lens spaces and orbifolds and similar locally symmetric spaces of rank one. Most of these results are related to those obtained by Lauret et al. (IMRN 2016(4):1054–1089, 2016. https://doi.org/10.1093/imrn/rnv159), where the spectra of lens spaces were described in terms of the one-norm spectrum of a naturally associated congruence lattice. As a consequence, the first examples of Riemannian manifolds isospectral on p-forms for all p but not strongly isospectral were constructed. We also give a new elementary proof in the case of the spectrum on functions. In this proof, representation theory of compact Lie groups is avoided and replaced by the use of Molien’s formula and a manipulation of the one-norm generating function associated to a congruence lattice. In the last four sections we present several recent results, open problems and conjectures on the subject.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
LENS SPACE
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SPECTRUM
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ISOSPECTRAL
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SPHERICAL HARMONIS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Recent results on the spectra of lens spaces
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-09-08T10:36:24Z
dc.identifier.eissn
2316-9028
dc.journal.volume
15
dc.journal.pagination
240-267
dc.journal.pais
Suiza
dc.description.fil
Fil: Lauret, Emilio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
dc.description.fil
Fil: Miatello, Roberto Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
dc.description.fil
Fil: Rossetti, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
dc.journal.title
São Paulo Journal of Mathematical Sciences
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s40863-019-00154-3
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s40863-019-00154-3
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