A note on functional independence of some
zeta-functions

Abstract. In the paper, we prove the joint denseness and the functional independence for the Dirichlet \(L\)-function \(L(s,\chi)\) and periodic Hurwitz zeta-function \(\zeta(s,\alpha;\mathfrak{b})\) with transcendental parameter \(\alpha\).

Key words and phrases. Density, Dirichlet \(L\)-function, functional independence, Hurwitz zeta-function, periodic coefficients, universality.