Rocky Mountain Journal of Mathematics

Phase calculations for planar partition polynomials

Robert P. Boyer and Daniel T. Parry

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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

Permanent link to this document
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

Subjects
Primary: 11C08: Polynomials [See also 13F20]
Secondary: 11M35: Hurwitz and Lerch zeta functions 30C55: General theory of univalent and multivalent functions 30E15: Asymptotic representations in the complex domain

Keywords
Asymptotic phase plane partition polylogarithm polynomials

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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References

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