Open AccessDiscrete universality of the Riemann zeta-function in short intervals
Author(s) -
Antanas Laurinčikas
Publication year - 2020
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm190704019l
Subject(s) - mathematics , universality (dynamical systems) , riemann zeta function , riemann hypothesis , combinatorics , pure mathematics , mathematical analysis , quantum mechanics , physics
We consider the approximation of analytic functions by shifts of the Riemann zeta-function ?(s+ikh) with fixed h > 0 when positive integers k run over the interval [N,N+M], where N1/3(logN)26=15 ? M ? N, and prove that those k have a positive lower density as N ? ?. The same is true for some compositions. Two types of h > 0 are discussed separately.