Open AccessGeometry and analysis of Shimizu L -functions
Author(s) -
Michael Atiyah,
Harold Donnelly,
I. M. Singer
Publication year - 1982
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.79.18.5751
Subject(s) - conjecture , mathematics , signature (topology) , pure mathematics , algebra over a field , geometry
The values of 0 of ShimizuL -functions are realized as the signature defects of framed manifolds. This settles a conjecture of Hirzebruch [Hirzebruch, F. (1973)Enseign. Math. 19, 183-281] affirmatively. The proof employs the spectral theory of elliptic operators.