On mixed joint discrete universality for a class of zeta-functions II

We study analytic properties of the pair consisting of a rather general form of zeta-function with an Euler product and a periodic Hurwitz zeta-function with a transcendental parameter. We first survey briefly previous results, and then investigate the mixed joint discrete value distribution and prove the mixed joint discrete universality theorem for these functions, in the case when common differences of relevant arithmetic progressions are not necessarily the same. Also some generalizations are given. For this purpose, certain arithmetic conditions on the common differences are necessary.