Joint universality and simple a-points of Lerch zeta-functions

摘要

For 0 1. We obtain the joint universality theorem for the collection of Lerch zeta-functions ∪_(j-1)~J {L (s, α_i, λ): 0 < λ ≤ 1}, when α_1,...,α_J satisfy a certain condition. This theorem is an improvement of several previous joint universality theorems for Lerch zeta-functions. We also investigate the distribution of simple a-points of Lerch zeta-functions and their derivatives.