Joint universality for dependent L-functions

Abstract

We prove that, for arbitrary Dirichlet L-functions L(s; χ1) , … , L(s; χn) (including the case when χj is equivalent to χk for j≠ k), suitable shifts of type L(s+iαjtajlogbjt;χj) can simultaneously approximate any given set of analytic functions on a simply connected compact subset of the right open half of the critical strip, provided the pairs (aj, bj) are distinct and satisfy certain conditions. Moreover, we consider a discrete analogue of this problem where t runs over the set of positive integers.