Multiple finite Riemann zeta functions

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.

19 pages

Cited by in corpus (2)

• Arithmetical properties of Multiple Ramanujan sums
• q-Analogues of the Barnes multiple zeta functions