Approximation in measure: the Dirichlet problem, universality and the Riemann hypothesis

Approximation in measure: the Dirichlet problem, universality and the Riemann hypothesis

We use approximation in measure to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann hypothesis are suggested.

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Veröffentlicht in:Izvestiya. Mathematics 2021-06, Vol.85 (3), p.547-561
Hauptverfasser: Falcó, J., Gauthier, P. M.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Asymptotic methods
Dirichlet problem
harmonic
harmonic approximation in measure
holomorphic
Hypotheses
Mathematical analysis
Riemann zeta-function
universality
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Beschreibung
Zusammenfassung:We use approximation in measure to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann hypothesis are suggested.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM9033