| Abstract: | We establish a joint universality theorem for Dirichlet L-functions in the character aspect. This is an extension of a result obtained by Bagchi and Gonek independently, and is an analogue of the joint universality for Dirichlet L-functions in the t-aspect. Zeros of linear combinations of Dirichlet L-functions in the t-aspect have been investigated by various authors. Using our joint universality theorem, we investigate zeros of such combinations from a new viewpoint. More precisely, we show that for any region \(\Omega \) in the strip \(1/2< \mathrm {Re}\,s <1\), any non-zero meromorphic functions \(H_1 (s), \dots , H_r(s)\) on \(\Omega \) with \(r \ge 2\) and any positive integer N, there exist a positive integer m and Dirichlet characters \(\varphi _1, \dots , \varphi _r \bmod m\) such that \(\sum _{j=1}^r H_j (s) L(s, \varphi _r)\) has at least N distinct zeros in \(\Omega \). |
