On q-analogues of Riemann's zeta
Quantum Algebra
2007-05-23 v3
Abstract
In the paper, we introduce -deformations of the Riemann zeta function, extend them to the whole complex plane, and establish certain estimates of the number of roots. The construction is based on the recent difference generalization of the Harish-Chandra theory of zonal spherical functions. We also discuss numerical results, which indicate that the location of the zeros of the -zeta functions is far from random.
Keywords
Cite
@article{arxiv.math/9804099,
title = {On q-analogues of Riemann's zeta},
author = {Ivan Cherednik},
journal= {arXiv preprint arXiv:math/9804099},
year = {2007}
}
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