This article is cited in 2 papers

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

J. Falcó^a, P. M. Gauthier<sup>b

a</sup> Departamento de Análisis Matemático, Universidad de Valencia, Burjasot (Valencia), Spain
^b Département de mathématiques et de statistique, Université de Montréal, Montréal, Québec, Canada

Abstract: 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.

Keywords: harmonic approximation in measure, harmonic, holomorphic, Dirichlet problem, Riemann zeta-function, universality.

UDC: 517.577+511.331

MSC: Primary 30K99, 30E10; Secondary 31C12, 11M06

Received: 13.03.2020
Revised: 12.06.2020

DOI: 10.4213/im9033

 English version: Izvestiya: Mathematics, 2021, 85:3, 547–561

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