Open AccessJoint approximation of analytic functions by shifts of the Riemann and periodic Hurwitz zeta-functions
Author(s) -
Antanas Laurinčikas,
Renata Macaitienė
Publication year - 2018
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/aadm170713016l
Subject(s) - mathematics , riemann hypothesis , riemann zeta function , independence (probability theory) , mathematical analysis , pure mathematics , rational number , field (mathematics) , riemann xi function , particular values of riemann zeta function , arithmetic zeta function , prime zeta function , statistics
We present some new results on the simultaneous approximation with given accuracy, uniformly on compact subsets of the critical strip, of a collection of analytic functions by discrete shifts of the Riemann and periodic Hurwitz zeta-functions. We prove that the set of such shifts has a positive lower density. For this, we apply the linear independence over the field of rational numbers of certain sets related to the zeta-functions.