Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros

Abstract

Assume the Riemann hypothesis. On the right-hand side of the critical strip, we obtain an asymptotic formula for the discrete mean square of the Riemann zeta-function over imaginary parts of its zeros.

Joint Discrete Approximation of a Pair of Analytic Functions by Periodic Zeta-Functions

“…The condition (1.4) was applied in [6] for the approximation of analytic functions by shifts ζ(s + iγ k h), in [30] for shifts ζ(s + iγ n h, α) and by shifts (ζ(s + iγ k h), ζ(s + iγ k h, α))) in [21]. In [4,5], in place of (1.4), the Riemann hypothesis was used. The paper [26] is devoted to joint approximation of analytic functions by shifts of Dirichlet L-functions L(s + iγ k h, χ 1 ), ..., L(s + iγ k h, χ r ) also by using (1.4).…”

Approximation of Analytic Functions by Shifts of Certain Compositions

“…Recall that the Riemann hypothesis (RH) asserts that all non-trivial zeros of ζ(s) lie on the critical line σ = 1/2. A similar result under RH was obtained in [28] by using moment estimates of [29]. Universality of the Hurwitz zeta-function with the sequence {γ k } satisfying (1) was considered in [30,31].…”