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Joint Discrete Universality in the Selberg–Steuding Class
- Source :
- Axioms, Vol 12, Iss 7, p 674 (2023)
- Publication Year :
- 2023
- Publisher :
- MDPI AG, 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 (hjlogp:p∈P),j=1,…,r;2π for positive hj, we obtain that there are many infinite shifts L(s+ikh1),…,L(s+ikhr), k=0,1,…, approximating every collection f1(s),…,fr(s) of analytic non-vanishing functions defined in the strip {s∈C:σL<σ<1}, where σL 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.
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 12
- Issue :
- 7
- Database :
- Directory of Open Access Journals
- Journal :
- Axioms
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.4db0880b01d144e5b3d57dc3cc66191f
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/axioms12070674