## Phase calculations for planar partition polynomials.(English)Zbl 1358.30002

Summary: 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 complex-valued functions constructed from polylogarithms, functions defined as $Li_s(z)=\sum_{n=1}^\infty \frac{z^{n}}{n^{s}}.$ These sets we call phases. This paper applies complex analytic techniques to describe the geometry of these sets in the complex plane.

### MSC:

 30B50 Dirichlet series, exponential series and other series in one complex variable 30C10 Polynomials and rational functions of one complex variable 30E15 Asymptotic representations in the complex plane 11P82 Analytic theory of partitions

### Keywords:

asymptotic; phase; plane partition; polylogarithm; polynomials
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### References:

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