We introduce the zeta Mahler measure with a complex parameter, whose derivative is a generalization of the classical Mahler measure. We study a fundamental theory of the zeta Mahler measure, including holomorphic regions and transformation formulas. We also express some specific examples of zeta Mahler measures in terms of hypergeometric functions

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We construct multiple zeta functions considered as absolute tensor products of usual zeta functions. We establish Euler product expressions for triple zeta functions [Formula: see text] with p, q, r distinct primes, via multiple sine functions by using the signatured Poisson summation formula. We also establish Euler product expressions for triple zeta functions [Formula: see text] with a prime p, via the theory of multiple sine functions.

In 1992 Deninger showed a version of explicit formulas for the Riemann zeta function. In this paper, we establish a duplication of Deninger's explicit formula in the sense of the absolute tensor product due to Kurokawa. As an application, we obtain an Euler product expression for the double Riemann zeta function constructed from the absolute tensor product of the Riemann zeta function.