Zeros and the universality for the Euler–Zagier–Hurwitz type of multiple zeta-functions

摘要

In this paper, we show relations between the zero-free region and the universality for the Euler–Zagier–Hurwitz type of multiple zeta-functions. Roughly speaking these relations imply that we can obtain the universality for the Euler–Zagier–Hurwitz type of multiple zeta-functions by their zero-free property, and vice versa. Moreover, we obtain the non-trivial zeros, joint denseness and functional independence for the Euler–Zagier–Hurwitz type of multiple zeta-functions.