MDPI - Publisher of Open Access Journals

14 pages, 302 KB

Open AccessFeature PaperArticle

by Antanas Laurinčikas and Darius Šiaučiūnas

Mathematics 2020, 8(11), 1936; https://doi.org/10.3390/math8111936 - 3 Nov 2020

Cited by 3 | Viewed by 2135

Let

0 < γ_{1} < γ_{2} < \dots ⩽ γ_{k} ⩽ \dots

be the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function

ζ (s)

. Using a certain estimate on the pair correlation of the [...] Read more.

Let

0 < γ_{1} < γ_{2} < \dots ⩽ γ_{k} ⩽ \dots

be the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function

ζ (s)

. Using a certain estimate on the pair correlation of the sequence

{γ_{k}}

in the intervals

[N, N + M]

with

N^{1 / 2 + ε} ⩽ M ⩽ N

, we prove that the set of shifts

ζ (s + i h γ_{k})

h > 0

, approximating any non-vanishing analytic function defined in the strip

{s \in C : 1 / 2 < Re s < 1}

with accuracy

ε > 0

has a positive lower density in

[N, N + M]

N \to \infty

. Moreover, this set has a positive density for all but at most countably

ε > 0

. The above approximation property remains valid for certain compositions

F (ζ (s))

. Full article

Search Results (1)