The universality of zeta-functions attached to certain cusp forms

Joint value-distribution theorems on Lerch zeta-functions. II

“…Thus, we have to show that the latter set is dense in H r (D 0 ). For this we will use Lemma 6 of [7].…”

On the Derivatives of Zeta-Functions of Certain Cusp Forms, Ii

“…Hence it follows easily that {ω 0 (p)} is also a sequence of independent random variables defined on the probability space ( 0 , B( 0 ), m 0H ). Therefore, the proof of the lemma coincides with that of [8,Lemma 8]. Proof.…”

“…From this and Lemma 4, using a modification of the Cramér-Wald criterion (see, for example, [4], [6], [7], [9]) we obtain that the probability measure…”

On the Derivatives of Zeta-Functions of Certain Cusp Forms

“…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]. Define on the probability space ( ,…”

“…Then by standard method (see, for example, [7], [6]), using Lemma 1 and Lemma 1 of [8], it can be proved that the probability measure…”