Sofic groups and diophantine approximation

Details Sofic groups and diophantine approximation Sofic groups and diophantine approximation

2007-01-10

arxiv.org/abs/math/0701294v3

Mathematics

Functional Analysis

15 pages, no figures

Scientific paper

We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V.
Mathai, T. Schick and S. Yates 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.

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