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- Q5402374 subject Q8376424.
- Q5402374 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.".
- Q5402374 wikiPageWikiLink Q1048264.
- Q5402374 wikiPageWikiLink Q1058681.
- Q5402374 wikiPageWikiLink Q1517914.
- Q5402374 wikiPageWikiLink Q190524.
- Q5402374 wikiPageWikiLink Q395.
- Q5402374 wikiPageWikiLink Q427625.
- Q5402374 wikiPageWikiLink Q4360731.
- Q5402374 wikiPageWikiLink Q5533833.
- Q5402374 wikiPageWikiLink Q564426.
- Q5402374 wikiPageWikiLink Q7496872.
- Q5402374 wikiPageWikiLink Q7512837.
- Q5402374 wikiPageWikiLink Q8376424.
- Q5402374 wikiPageWikiLink Q973313.
- Q5402374 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.".
- Q5402374 label "Eta invariant".