  Given a frequency $\lambda$, we study general Dirichlet series $\sum a_n
e^{-\lambda_n s}$. First, we give a new condition on $\lambda$ which ensures
that a somewhere convergent Dirichlet series defining a bounded holomorphic
function in the right half-plane converges uniformly in this half-plane,
improving classical results of Bohr and Landau. Then, following recent works of
Defant and Schoolmann, we investigate Hardy spaces of these Dirichlet series.
We get general results on almost sure convergence which have an harmonic
analysis flavour. Nevertheless, we also exhibit examples showing that it seems
hard to get general results on these spaces as spaces of holomorphic functions.
