## Rocky Mountain Journal of Mathematics

### Phase calculations for planar partition polynomials

#### Abstract

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.

#### Article information

Source
Rocky Mountain J. Math., Volume 44, Number 1 (2014), 1-18.

Dates
First available in Project Euclid: 2 June 2014

https://projecteuclid.org/euclid.rmjm/1401740487

Digital Object Identifier
doi:10.1216/RMJ-2014-44-1-1

Mathematical Reviews number (MathSciNet)
MR3216005

Zentralblatt MATH identifier
1358.30002

#### Citation

Boyer, Robert P.; Parry, Daniel T. Phase calculations for planar partition polynomials. Rocky Mountain J. Math. 44 (2014), no. 1, 1--18. doi:10.1216/RMJ-2014-44-1-1. https://projecteuclid.org/euclid.rmjm/1401740487

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