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- Eta_invariant abstract "In mathematics, the eta invariant of a self-adjoint elliptic differential operator on a compact manifold is formally the number of positive eigenvalues minus the number of negative eigenvalues. In practice both numbers are often infinite so are defined using zeta function regularization. It was introduced by Atiyah, Patodi, and Singer (1973, 1975) who used it to extend the Hirzebruch signature theorem to manifolds with boundary. The name comes from the fact that it is a generalization of the Dirichlet eta function.They also later used the eta invariant of a self-adjoint operator to define the eta invariant of a compact odd-dimensional smooth manifold.Michael Francis Atiyah, H. Donnelly, and I. M. Singer (1983)defined the signature defect of the boundary of a manifold as the eta invariant, and used this to show that Hirzebruch's signature defect of a cusp of a Hilbert modular surface can be expressed in terms of the value at s=0 or 1 of a Shimizu L-function.".
- Eta_invariant wikiPageID "35063240".
- Eta_invariant wikiPageLength "2997".
- Eta_invariant wikiPageOutDegree "14".
- Eta_invariant wikiPageRevisionID "679061815".
- Eta_invariant wikiPageWikiLink Annals_of_Mathematics.
- Eta_invariant wikiPageWikiLink Category:Differential_operators.
- Eta_invariant wikiPageWikiLink Closed_manifold.
- Eta_invariant wikiPageWikiLink Differential_operator.
- Eta_invariant wikiPageWikiLink Dirichlet_eta_function.
- Eta_invariant wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Eta_invariant wikiPageWikiLink Elliptic_operator.
- Eta_invariant wikiPageWikiLink Genus_of_a_multiplicative_sequence.
- Eta_invariant wikiPageWikiLink Hilbert_modular_surface.
- Eta_invariant wikiPageWikiLink Mathematics.
- Eta_invariant wikiPageWikiLink Shimizu_L-function.
- Eta_invariant wikiPageWikiLink Signature_defect.
- Eta_invariant wikiPageWikiLink Zeta_function_regularization.
- Eta_invariant wikiPageWikiLinkText "eta invariant".
- Eta_invariant author1Link "Michael Atiyah".
- Eta_invariant author2Link "Vijay Kumar Patodi".
- Eta_invariant author3Link "Isadore Singer".
- Eta_invariant doi "10.2307".
- Eta_invariant first "H.".
- Eta_invariant first "I. M.".
- Eta_invariant first "Michael Francis".
- Eta_invariant issn "3".
- Eta_invariant issue "1".
- Eta_invariant journal Annals_of_Mathematics.
- Eta_invariant last "Atiyah".
- Eta_invariant last "Donnelly".
- Eta_invariant last "Patodi".
- Eta_invariant last "Singer".
- Eta_invariant mr "707164".
- Eta_invariant pages "131".
- Eta_invariant title "Eta invariants, signature defects of cusps, and values of L-functions".
- Eta_invariant volume "118".
- Eta_invariant wikiPageUsesTemplate Template:Citation.
- Eta_invariant wikiPageUsesTemplate Template:Harvs.
- Eta_invariant year "1973".
- Eta_invariant year "1975".
- Eta_invariant year "1983".
- Eta_invariant subject Category:Differential_operators.
- Eta_invariant comment "In mathematics, the eta invariant of a self-adjoint elliptic differential operator on a compact manifold is formally the number of positive eigenvalues minus the number of negative eigenvalues. In practice both numbers are often infinite so are defined using zeta function regularization. It was introduced by Atiyah, Patodi, and Singer (1973, 1975) who used it to extend the Hirzebruch signature theorem to manifolds with boundary.".
- Eta_invariant label "Eta invariant".
- Eta_invariant sameAs Q5402374.
- Eta_invariant sameAs エータ不変量.
- Eta_invariant sameAs m.0j65wf2.
- Eta_invariant sameAs Q5402374.
- Eta_invariant wasDerivedFrom Eta_invariant?oldid=679061815.
- Eta_invariant isPrimaryTopicOf Eta_invariant.