Multiple finite Riemann zeta functions

Details Multiple finite Riemann zeta functions Multiple finite Riemann zeta functions

2004-04-07

arxiv.org/abs/math/0404144v1

Acta Arith. 116 (2005), 173-187

Mathematics

Number Theory

19 pages

Scientific paper

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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