On the asymptotic behavior of unimodal rank generating functions
Kathrin Bringmann, Byungchan Kim
TL;DR
This paper proves asymptotic versions of conjectured inequalities for ranks of unimodal sequences by extending Wright's Circle Method and analyzing partial theta functions.
Contribution
It extends Wright's Circle Method to analyze the asymptotic behavior of partial theta functions related to unimodal sequence ranks.
Findings
Proved conjectured inequalities asymptotically for four types of unimodal sequences.
Extended Wright's Circle Method for analyzing partial theta functions.
Provided new insights into the asymptotic behavior of unimodal rank generating functions.
Abstract
In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we extend Wright's Circle Method and analyze the asymptotic behavior of certain general partial theta functions.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Analytic Number Theory Research