Nonmodular infinite products and a conjecture of Seo and Yee

We will tackle a conjecture of S. Seo and A. J. Yee, which says that the series expansion of 1/(q,−q3;q4)∞ has nonnegative coefficients. Our approach relies on an approximation of the generally nonmodular infinite product 1/(qa;qM)∞, where M is a positive integer and a is any of 1,2,…,M.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2023-03, Vol.417, p.108932, Article 108932
Main Author: Chern, Shane
Format: Article
Language:English
Subjects:
Asymptotic formula
Circle method
Inverse Mellin transform
Nonmodular infinite product
Seo–Yee conjecture
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Summary:We will tackle a conjecture of S. Seo and A. J. Yee, which says that the series expansion of 1/(q,−q3;q4)∞ has nonnegative coefficients. Our approach relies on an approximation of the generally nonmodular infinite product 1/(qa;qM)∞, where M is a positive integer and a is any of 1,2,…,M.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.108932