The concept of quasi-periodic property of a function has been introduced by\nHarald Bohr in 1921 and it roughly means that the function comes (quasi)-\nperiodically as close as we want on every vertical line to the value taken by\nit at any point belonging to that line and a bounded domain... He proved\nthat the functions defined by ordinary Dirichlet series are quasi-periodic in\ntheir half plane of uniform convergence. We realized that the existence of the\ndomain... is not necessary and that the quasi-periodicity is related to the\ndenseness property of those functions which we have studied in a previous\npaper. Hence, the purpose of our research was to prove these two facts. We\nsucceeded to fulfill this task and more. Namely, we dealt with the quasi-\nperiodicity of general Dirichlet series by using geometric tools perfected by\nus in a series of previous projects. The concept has been applied to the whole\ncomplex plane (not only to the half plane of uniform convergence) for series\nwhich can be continued to meromorphic functions in that plane. The question\narise: in what conditions such a continuation is possible? There are\nknown examples of Dirichlet series which cannot be continued across the\nconvergence line, yet there are no simple conditions under which such a continuation\nis possible. We succeeded to find a very natural one.
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