Joint universality for Lerch zeta-functions

Abstract

For 0 < α, λ ≤ 1, the Lerch zeta-function is defined by L(s; α, λ) := ∑^∞_n=0 e^2πiλn (n + α)^−s, where σ > 1. In this paper, we prove joint universality for Lerch zeta-functions with distinct λ₁,…,λ_m and transcendental α.