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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 qq-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.

Keywords

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}
}

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19 pages