Resumen de Analytic continuation of Dirichlet series

J. M. Anderson, Dmitry Khavinson, H. S. Shapiro

• The questions considered in this paper arose from the study [KS] of I. Fredholm's (insufficient) proof that the gap series S08 an ?n2 (where 0 < |a| < 1) is nowhere continuable across {|?| = 1}. The interest of Fredholm's method ([F],[ML]) is not so much its efficacy in proving gap theorems (indeed, much more general results can be got by other means, cf. the Fabry gap theorem in [Di]) as in the connection it made between certain special gap series and partial differential equations (...).