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Regularized and L 2 ‐Determinants
Author(s) -
Deitmar A
Publication year - 1998
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611598000057
Subject(s) - mathematics , euler's formula , pure mathematics , product (mathematics) , mathematics subject classification , torsion (gastropod) , tower , algebra over a field , mathematical analysis , geometry , medicine , civil engineering , engineering , surgery
A notion of L 2 ‐determinant is established generalizing L 2 ‐torsion. It is shown that classical regularized determinants of elliptic operators converge to L 2 ‐determinants in a tower of coverings. A product formula is proved, which provides an Euler‐product expansion to regularized determinants, having generalized L 2 ‐determinants as Euler‐factors. 1991 Mathematics Subject Classification : 58G26, 58F20.