On q-analogues of Riemann's zeta

Details On q-analogues of Riemann's zeta On q-analogues of Riemann's zeta

1998-04-21

arxiv.org/abs/math/9804099v3

Mathematics

Quantum Algebra

AMSTeX

Scientific paper

In the paper, we introduce $q$-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 $q$-zeta functions is far from random.

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