The joint universality of twisted automorphic \(L\)-functions. (English) Zbl 1142.11032

Laurinčikas, Antanas; Matsumoto, Kohji

J. Math. Soc. Japan 56, No. 3, 923-939 (2004).

Summary: The simultaneous universality of twisted automorphic \(L\)-functions, associated with a new form with respect to a congruence subgroup of \(\text{SL}(2, \mathbb Z)\) and twisted by Dirichlet characters, is proved. Applications to the functional independence and the zero density of linear combinations of those \(L\)-functions are given.

MSC:

11F66	Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F11	Holomorphic modular forms of integral weight
11F25	Hecke-Petersson operators, differential operators (one variable)