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

Antanas Laurinčikas and Renata Macaitienė ()
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Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
Renata Macaitienė: Faculty of Business and Technologies, Šiauliai State Higher Education Institution, Aušros Av. 40, LT-76241 Šiauliai, Lithuania

Mathematics, 2023, vol. 11, issue 11, 1-12

Abstract: In the paper, the approximation of analytic functions on compact sets of the strip { s = σ + i t ∈ C ∣ 1 / 2 < σ < 1 } by shifts F ( ζ ( s + i u 1 ( τ ) ) , … , ζ ( s + i u r ( τ ) ) ) , where ζ ( s ) is the Riemann zeta-function, u 1 , … , u r 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.

Keywords: Riemann zeta-function; space of analytic functions; joint universality; weak convergence of probability measures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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