Multiple finite Riemann zeta functions
Number Theory
2015-06-26 v1
Abstract
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some -series identity for proving the zeta function has an Euler product and then, describe the location of zeros. We study further multi-variable and multi-parameter versions of the multiple finite Riemann zeta functions and their infinite counterparts in connection with symmetric polynomials and some arithmetic quantities called powerful numbers.
Cite
@article{arxiv.math/0404144,
title = {Multiple finite Riemann zeta functions},
author = {K. Kimoto and N. Kurokawa and S. Matsumoto and M. Wakayama},
journal= {arXiv preprint arXiv:math/0404144},
year = {2015}
}
Comments
19 pages