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This remarkable result raised much attention among specialists, and Reich [18], [19], Gonek [4], Good [5], Bagchi [1], [2], and the first author [8]-[12], [14] improved and generalized the Voronin theorem to various other Dirichlet series including Dirichlet L , and Dedekind, Hurwitz, and Lerch zeta-functions. It is the purpose of the present paper to prove the universality theorem for zetafunctions attached to certain cusp forms. Let F (z) be a holomorphic cusp form of weight κ for the full modular group SL(2, Z) , and assume that F (z) is a normalized eigenform. Then F (z) has the Fourier series expansion

The universality of zeta-functions attached to certain cusp forms