A note on Bohr’s theorem for Beurling integer systems
dc.contributor.author | Broucke, Frederik | |
dc.contributor.author | Kouroupis, Athanasios | |
dc.contributor.author | Perfekt, Karl-Mikael | |
dc.date.accessioned | 2024-01-15T09:26:07Z | |
dc.date.available | 2024-01-15T09:26:07Z | |
dc.date.created | 2023-11-28T11:46:23Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Mathematische Annalen 2023 | en_US |
dc.identifier.issn | 0025-5831 | |
dc.identifier.uri | https://hdl.handle.net/11250/3111444 | |
dc.description.abstract | Given a sequence of frequencies , a corresponding generalized Dirichlet series is of the form . We are interested in multiplicatively generated systems, where each number arises as a finite product of some given numbers , , referred to as Beurling primes. In the classical case, where , Bohr’s theorem holds: if f converges somewhere and has an analytic extension which is bounded in a half-plane , then it actually converges uniformly in every half-plane , . We prove, under very mild conditions, that given a sequence of Beurling primes, a small perturbation yields another sequence of primes such that the corresponding Beurling integers satisfy Bohr’s condition, and therefore the theorem. Applying our technique in conjunction with a probabilistic method, we find a system of Beurling primes for which both Bohr’s theorem and the Riemann hypothesis are valid. This provides a counterexample to a conjecture of H. Helson concerning outer functions in Hardy spaces of generalized Dirichlet series. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | A note on Bohr’s theorem for Beurling integer systems | en_US |
dc.title.alternative | A note on Bohr’s theorem for Beurling integer systems | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.journal | Mathematische Annalen | en_US |
dc.identifier.doi | 10.1007/s00208-023-02756-x | |
dc.identifier.cristin | 2203662 | |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 |
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