Effective Universality Theorem: A Survey

Garunkštis, Ramūnas; Laurinčikas, Antanas

doi:10.1007/s10986-021-09533-w

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Introduction1

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2022

2023

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Cited by 2 publications

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“…Good [15]; R. Garunkštis applied and developed Good's ideas for the effective approximation of analytic functions in small discs [16]. The mentioned and other effective results connected to the universality of zeta-functions can be found in the survey paper [17]. In this regard, we note that (1) is implied by its short interval version, i.e., with I T replaced by [T, 2T].…”

Section: Introductionmentioning

confidence: 93%

Generalized Universality for Compositions of the Riemann Zeta-Function in Short Intervals

Laurinčikas

Macaitienė

2023

Mathematics

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In the paper, the approximation of analytic functions on compact sets of the strip {s=σ+it∈C∣1/2<σ<1} by shifts F(ζ(s+iu1(τ)),⋯,ζ(s+iur(τ))), where ζ(s) is the Riemann zeta-function, u1,⋯,ur are certain differentiable increasing functions, and F is a certain continuous operator in the space of analytic functions, is considered. It is obtained that the set of the above shifts in the interval [T,T+H] with H=o(T), T→∞, has a positive lower density. Additionally, the positivity of a density with a certain exceptional condition is discussed. Examples of considered operators F are given.

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Section: Introductionmentioning

confidence: 93%