Voronin Universality in several complex variables

Abstract

We prove the Voronin universality theorem for the multiple Hurwitz zeta-function with rational or transcendental parameters in ${\mathbb{C}}^n$ answering a question of Matsumoto. In particular this implies that the Euler-Zagier multiple zeta-function is universal in several complex variables and gives the first example of a Dirichlet series that is universal in more than one variable.

v1: 100 pages; v2: 90 pages. For changes from v1, see p.3-p.4 of the paper

References in corpus (4)

• Approximation in C^N
• A remark on approximation on totally real sets
• On the universality of the Epstein zeta function
• On questions of Cassels and Drungilas-Dubickas

Cited by in corpus (1)

• Universality of the Hurwitz zeta-function on the half plane of absolute convergence