On generalized Hardy classes of Dirichlet series

Abstract

We generalize the Hardy class H^2 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 L^1-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.

31 pages

References in corpus (3)

• On the zeta function on the line Re(s) = 1
• On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate
• On a problem of Ramachandra and approximation of functions by Dirichlet polynomials with bounded coefficients

Cited by in corpus (2)

• On the zeta function on the line Re(s) = 1
• On a problem of Ramachandra and approximation of functions by Dirichlet polynomials with bounded coefficients