The universality of $L$-functions attached to Maass forms

Abstract

We establish the universality theorem on the strip $\{ s \in \mathbb{C} | 1/2 \lt \mathrm{Re}\ s \lt 1\}$ for automorphic $L$-functions attached to Maass forms for $SL(2, \mathbb{Z})$, without the assumption of the Ramanujan conjecture. From this theorem, some results concerning the value distribution of the derivatives of those $L$-functions are obtained.