symmetric monoidal (∞,1)-category of spectra
(…)
Given a totally real algebraic number field , a lattice on it and a subgroup of maximal rank of the subgroup of totally positive units preserving the lattice, its Shimizu L-function is given by:
Michael Atiyah, Harold Donnelly and Isadore Singer defined the signature defect of the boundary of a manifold as the eta invariant, the value at of their eta function, and used this to show that Hirzebruch’s signature defect of a cusp of a Hilbert modular variety can be expressed in terms of the value at or of a Shimizu L-function.
The notion is due to:
Further developments:
Michael Atiyah, Harold Donnelly, Isadore Singer: Geometry and analysis of Shimizu L-functions, Proceedings of the National Academy of Sciences of the United States of America. 79 18 (1982) 5751 [ISSN 0027-8424, doi:10.1073/pnas.79.18.5751, PMID 16593231, PMC 346984, bibcode:1982PNAS…79.5751A, jstor:12685]
Michael Atiyah, Harold Donnelly, Isadore Singer: Eta invariants, signature defects of cusps, and values of L-functions, Annals of Mathematics. 118 1 (1982) 131–177 [ISSN 0003-486X, doi:10.2307/2006957, jstor:2006957]
See also:
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