On generalized Hardy classes of Dirichlet series

2012/07/23 by Johan Andersson, Andersson, Johan · 1 citation
Mathematics · #Analytic Number Theory Research #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1207.5337

Abstract

We generalize the Hardy class H² of Dirichlet series studied by Hedenmalm, Lindqvist, Olofsson, Olsen, Saksman, Seip and others to consider more general Dirichlet series. We prove some results on this class, such as estimates for its logarithmic L¹-norm in short intervals. We relate this to, and use these results to make a recent nonvanishing result of Dirichlet series of ours more explicit. In particular we give an application on the Hurwitz zeta-function.

Citations

• Hilbert's Inequality

Cited by

• Non universality on the critical line
• Universality of the Hurwitz zeta-function on the half plane of absolute convergence
• On a problem of Ramachandra and approximation of functions by Dirichlet polynomials with bounded coefficients

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