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2014 Phase calculations for planar partition polynomials
Robert P. Boyer, Daniel T. Parry
Rocky Mountain J. Math. 44(1): 1-18 (2014). DOI: 10.1216/RMJ-2014-44-1-1

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.

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Robert P. Boyer. Daniel T. Parry. "Phase calculations for planar partition polynomials." Rocky Mountain J. Math. 44 (1) 1 - 18, 2014. https://doi.org/10.1216/RMJ-2014-44-1-1

Information

Published: 2014
First available in Project Euclid: 2 June 2014

zbMATH: 1358.30002
MathSciNet: MR3216005
Digital Object Identifier: 10.1216/RMJ-2014-44-1-1

Subjects:
Primary: 11C08
Secondary: 11M35 , 30C55 , 30E15

Keywords: asymptotic , phase , Plane partition , polylogarithm , polynomials

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.44 • No. 1 • 2014
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