Asymptotic enumeration by Khintchine-Meinardus method: Necessary and   sufficient conditions for sub exponential growth
  In this paper we prove the necessity of the main sufficient condition of Meinardus for sub exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary and suffcient condition for normal local limit theorem for aforementioned structures. The latter result allows to encompass in our study structures with weights having gaps in their supports. 
Boris Granovsky
math.CO