Asymptotic expansions for partitions generated by infinite products.

Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in Λ ⊂ N ( gcd (Λ) = 1 ) and good analytic properties of the corresponding zeta function, generalizing work of Meinardus. In this paper, we extend their work to prove asymptotic formulas if Λ is a multiset of integers and the zeta function has multiple poles. In particular, our results imply an asymptotic formula for the number of irreducible representations of degree n of so (5) . We also study the Witten zeta function ζ so (5) , which is of independent interest. [ABSTRACT FROM AUTHOR]