Joint discrete mixed universality of \(L\)-functions
of new forms and periodic Hurwitz zeta-function

Abstract. In the paper, we study the analytic properties of the pair consisting of the \(L\)-functions of new forms and periodic Hurwitz zeta-functions with a transcendental parameter, i.e., we investigate the mixed joint discrete value distribution of this tuple in two cases. For this purpose, certain arithmetical conditions are used. Also, we give some applications of these limit theorems.

Key words and phrases. Arithmetic progression, joint approximation, Hurwitz zeta-function,
\(L\)-function, new forms, periodic coefficients, probability measure, value distribution, weak convergence, universality.