Estimates for spectral density functions of matrices over C[Z^d]
Number Theory
2014-10-30 v2
Abstract
We give a polynomial bound on the spectral density function of a matrix over the complex group ring of Z^d. It yields an explicit lower bound on the Novikov-Shubin invariant associated to this matrix showing in particular that the Novikov-Shubin invariant is larger than zero.
Cite
@article{arxiv.1310.8564,
title = {Estimates for spectral density functions of matrices over C[Z^d]},
author = {Wolfgang Lueck},
journal= {arXiv preprint arXiv:1310.8564},
year = {2014}
}
Comments
11 pages, to appear in Annales Mathematiques Blaise Pascal, final version. We have taken out in the earlier version the algorithm for computing the Mahler measure since there are better ones in the literature