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 (5)

• Mergelyan's approximation theorem with nonvanishing polynomials and universality of zeta-functions
• 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
• Non universality on the critical line
• On a problem of Ramachandra and approximation of functions by Dirichlet polynomials with bounded coefficients

Cited by in corpus (5)

• 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
• Non universality on the critical line
• Universality of the Hurwitz zeta-function on the half plane of absolute convergence
• On the Balasubramanian-Ramachandra method close to Re(s)=1