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Joint Discrete Approximation of Analytic Functions by Shifts of the Riemann Zeta Function Twisted by Gram Points II.
- Source :
-
Axioms (2075-1680) . May2023, Vol. 12 Issue 5, p426. 14p. - Publication Year :
- 2023
-
Abstract
- In this paper, a theorem is obtained on the approximation in short intervals of a collection of analytic functions by shifts (ζ (s + i t k α 1) , ... , ζ (s + i t k α r)) of the Riemann zeta function. Here, { t k : k ∈ N } is the sequence of Gram numbers, and α 1 , ... , α r are different positive numbers not exceeding 1. It is proved that the above set of shifts in the interval [ N , N + M ] , here M = o (N) as N → ∞ , has a positive lower density. For the proof, a joint limit theorem in short intervals for weakly convergent probability measures is applied. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ANALYTIC functions
*PROBABILITY measures
*LIMIT theorems
*ZETA functions
Subjects
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 12
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 163953420
- Full Text :
- https://doi.org/10.3390/axioms12050426