PHASE CALCULATIONS FOR PLANAR PARTITION POLYNOMIALS

摘要

In the study of the asymptotic behavior of polynomials from partition theory, the determination of their leading term asymptotics inside the unit disk depends on a sequence of sets derived from comparing certain complexvalued functions constructed from polylogarithms, functions defined as Lis(z) =∑~∞_(n=1)z~n~s. These sets we call phases. This paper applies complex analytic techniques to describe the geometry of these sets in the complex plane.