Sofic groups and diophantine approximation

Abstract

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.

15 pages, no figures