On dirichlet series related to certain cusp forms

The universality of zeta-functions attached to certain cusp forms

“…Kačėnas-Laurinčikas [7] proved this limit theorem on the space H( D), where D = {s ∈ C : σ > κ/2}, from which Lemma 1 follows immediately. Lemma 1 can also be regarded as a special case of the result proved in [13].…”

“…A classical result of Hecke [6] Before the present work, the universality of ϕ(s, F ) was obtained by Kačėnas-Laurinčikas [7], and also as a special case of the theorem given in [15], but both papers require rather strong assumptions. For instance, the universality theorem of Kačėnas-Laurinčikas [7] is proved under the assumption of the existence of η > 0 such that .…”

“…For instance, the universality theorem of Kačėnas-Laurinčikas [7] is proved under the assumption of the existence of η > 0 such that . However it seems to be hopeless to verify (1.1).…”

On the Derivatives of Zeta-Functions of Certain Cusp Forms

“…We shall use a limit theorem in the space of analytic functions for the function ϕ(s; F). Such a theorem in the space H( D), where D = {s ∈ ‫ރ‬ : σ > κ 2 }, was proved in [3]. However, we consider the space H(D V ), therefore we will apply Lemma 1 from [8].…”

A Limit Theorem for the Arguments of Zeta-Functions of Certain Cusp Forms

“…A modern limit theorem in the space of analytic functions H (D), D = {s : C : κ/2 < σ < (κ + 1)/2} for the function ϕ(s, F ) is proved in [4]; more precisely, it is proved that the probability measures…”