This is an announcement for the paper "Almost sure-sign convergence of Hardy-type Dirichlet series" by Daniel Carando, Andreas Defant, and Pablo Sevilla-Peris.
Abstract: Hartman proved in 1939 that the width of the largest possible strip in the complex plane, on which a Dirichlet series $\sum_n a_n n^{-s}$ is uniformly a.s.-sign convergent (i.e., $\sum_n \varepsilon_n a_n n^{-s}$ converges uniformly for almost all sequences of signs $\varepsilon_n =\pm 1$) but does not convergent absolutely, equals $1/2$. We study this result from a more modern point of view within the framework of so called Hardy-type Dirichlet series with values in a Banach space.
Archive classification: math.FA
Mathematics Subject Classification: 30B50, 30H10, 46G20
Submitted from: dcarando@dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.5030
or