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For a general Dirichlet series $\sum a_n e^{-\lambda_n s}$ with frequency$\lambda=(\lambda_n)_n$, we study how horizontal translation (i.e. convolutionwith a Poisson kernel) improves its integrability properties. We characterizehypercontractive frequencies in terms of their additive structure answeringsome questions posed by Bayart. We also provide sharp bounds for the strips$S_p(\lambda)$ that encode the minimum translation necessary for series in theHardy space $\mathcal{H}_p(\lambda)$ to have absolutely convergentcoefficients.

Hypercontractivity and strips of convergence in Hardy spaces of general Dirichlet series