Functional distribution for a collection of Lerch zeta functions

Abstract

Let 0 < α < 1 be a transcendental real number and λ₁, …, λ_r be real numbers with 0 ≤ λ_j < 1. It is conjectured that a joint universality theorem for a collection of Lerch zeta functions {L(λ_j,α,s)} will hold for every numbers λ_j's which are different each other. In this paper we will prove that the joint universality theorem for the set {L(λ_j,α,s)} holds for almost all real numbers λ_j's.