Joint approximation of analytic functions by shifts of the Riemann and periodic Hurwitz zeta-functions
Copyright policy )Joint approximation of analytic functions by shifts of the Riemann and periodic Hurwitz zeta-functions
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.
- Vilnius University Lithuania
- Šiauliai University Lithuania
Haar measure, Mergelyan theorem, \(\zeta (s)\) and \(L(s, \chi)\), periodic Hurwitz zeta-function, universality, Other Dirichlet series and zeta functions, Approximation by other special function classes, Riemann zeta-function
Haar measure, Mergelyan theorem, \(\zeta (s)\) and \(L(s, \chi)\), periodic Hurwitz zeta-function, universality, Other Dirichlet series and zeta functions, Approximation by other special function classes, Riemann zeta-function
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).3 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!