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Sofic groups and diophantine approximation
Author(s) -
Thom Andreas
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20217
Subject(s) - mathematics , conjecture , algebraic number , diophantine equation , group (periodic table) , pure mathematics , eigenvalues and eigenvectors , group ring , discrete mathematics , algebra over a field , mathematical analysis , chemistry , organic chemistry , physics , quantum mechanics
We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known that is not sofic. © 2007 Wiley Periodicals, Inc.