The translation operator in spaces of Dirichlet series

In this talk we explore different ideas and results concerning the convergence of Dirichlet series and horizontal translations. We will begin with a historical overview of the subject, starting with some ideas of Bohr from the early 20th century and some elementary examples. We will then see how horizontal translations improve both convergence and integrability properties. Then, we will present some new results obtained in collaboration with Andreas Defant, Felipe Marceca, Pablo Sevilla Peris and Ingo Schoolmann on Hardy spaces of general Dirichlet series.