Some topics related to universality of L-functions with an Euler product
Abstract In this paper, we show the joint universality of the set of the Steuding class L-functions {L(s+iδlτ)}l=1m for almost all (δ1,…,δm)∈Rm. From this property, we obtain the result that {L(s+iδlτ)}l=j,k, where δj and δk are two of the above, has a kind of generalized strong recurrence. Roughly speaking, this means that L(s+iδjτ) can be uniformly approximated by L(s+iδkτ) in the sense of universality. Moreover, we consider the relation between the generalized strong recurrence and zeros of the Selberg and Steuding class L-functions L(s). Finally, we obtain the upper bound for the density of universality for the Steuding class L-functions.