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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. 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 wikiPageRevisionID "604228737".
- 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 hasPhotoCollection Eta_invariant.
- 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 year "1973".
- Eta_invariant year "1975".
- Eta_invariant year "1983".
- Eta_invariant subject Category:Differential_operators.
- Eta_invariant type Abstraction100002137.
- Eta_invariant type DifferentialOperators.
- Eta_invariant type Function113783816.
- Eta_invariant type MathematicalRelation113783581.
- Eta_invariant type Operator113786413.
- Eta_invariant type Relation100031921.
- 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 m.0j65wf2.
- Eta_invariant sameAs Q5402374.
- Eta_invariant sameAs Q5402374.
- Eta_invariant sameAs Eta_invariant.
- Eta_invariant wasDerivedFrom Eta_invariant?oldid=604228737.
- Eta_invariant isPrimaryTopicOf Eta_invariant.