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Multiple finite Riemann zeta functions

K. Kimoto·N. Kurokawa·S. Matsumoto·M. Wakayama
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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 $q$-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.

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K. Kimoto, N. Kurokawa, S. Matsumoto, M. Wakayama. 2004-04-07. Multiple finite Riemann zeta functions. https://doi.org/10.4064/aa116-2-5

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