Joint approximation of analytic functions by shifts of the Riemann and periodic Hurwitz zeta-functions | Zendy

Antanas Laurinčikas | Zendy; Renata Macaitienė | Zendy

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Joint 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.

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