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Joint Discrete Universality in the Selberg–Steuding Class.
- Source :
-
Axioms (2075-1680) . Jul2023, Vol. 12 Issue 7, p674. 14p. - Publication Year :
- 2023
-
Abstract
- In the paper, we consider the approximation of analytic functions by shifts from the wide class S ˜ of L-functions. This class was introduced by A. Selberg, supplemented by J. Steuding, and is defined axiomatically. We prove the so-called joint discrete universality theorem for the function L (s) ∈ S ˜ . Using the linear independence over Q of the multiset (h j log p : p ∈ P) , j = 1 , ... , r ; 2 π for positive h j , we obtain that there are many infinite shifts L (s + i k h 1) , ... , L (s + i k h r) , k = 0 , 1 , ... , approximating every collection f 1 (s) , ... , f r (s) of analytic non-vanishing functions defined in the strip { s ∈ C : σ L < σ < 1 } , where σ L is a degree of the function L (s) . For the proof, the probabilistic approach based on weak convergence of probability measures in the space of analytic functions is applied. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 12
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 168599597
- Full Text :
- https://doi.org/10.3390/axioms12070674