Signature defects of cusps and values of L-functions: The nonsplit case
type: Item
instance of: scholarly article
title: Signature defects of cusps and values of L-functions: The nonsplit case
zbMATH Open document ID: 0577.58030
DOI: 10.2307/2007088
author: Michael Atiyah
author: Harold Donnelly
author: I. M. Singer
published in: Annals of Mathematics. Second Series
publication date: 1984-01-01T00:00:00Z
review text: This note is a supplement to our paper [Ann. Math., II. Ser. 118, 131-177 (1983; Zbl 0531.58048)]. Hirzebruch conjectured that the values at zero of the Shimizu L-functions are realized as the signature defects of cusps associated to Hilbert modular varieties. In the paper cited above we claimed to have established the Hirzebruch conjecture but, as was pointed out to us by W. Müller, we only dealt with the ''split'' case. In fact our method of proof extends with essentially no change to the non-split case.
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 11F41
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11R52
Mathematics Subject Classification ID: 11R80
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14J25
zbMATH DE Number: 3923732
zbMATH Keywords: eta invariants
zbMATH Keywords: signature defects of cusps
zbMATH Keywords: special values of
zbMATH Keywords: L- functions
zbMATH Keywords: cusp on Hilbert modular variety
zbMATH Keywords: lattice in totally
zbMATH Keywords: real field
zbMATH Keywords: Hirzebruch L-polynomial
zbMATH Keywords: Hirzebruch
zbMATH Keywords: signature theorem
zbMATH Keywords: flat connection
zbMATH Keywords: Feynman-Kac
zbMATH Keywords: representation of the heat kernel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2007088
OpenAlex ID: W2321231007
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description: scientific article; zbMATH DE number 3923732