Rocky Mountain Journal of Mathematics

Phase calculations for planar partition polynomials

Robert P. Boyer and Daniel T. Parry

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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

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

First available in Project Euclid: 2 June 2014

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Zentralblatt MATH identifier

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

Asymptotic phase plane partition polylogarithm polynomials


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.

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