Generalization of the Wiener-Ikehara theorem
  We study the Wiener-Ikehara theorem under the so-called log-linearly slowly decreasing condition. Moreover, we clarify the connection between two different hypotheses on the Laplace transform occurring in exact forms of the Wiener-Ikehara theorem, that is, in "if and only if" versions of this theorem. 
Gregory Debruyne and Jasson Vindas
math.NT math.CA