Taylor coefficients of false Jacobi forms and ranks of unimodal sequences

Taylor coefficients of false Jacobi forms and ranks of unimodal sequences

We apply the new framework for modularity of false theta functions developed by the second author and Nazaroglu to study the asymptotic behavior of Taylor coefficients of false Jacobi forms. The examples we study generate moments of the rank for unimodal sequences. For two types of unimodal sequence...

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Veröffentlicht in:Advances in mathematics (New York. 1965) 2023-08, Vol.426, p.109074, Article 109074
Hauptverfasser: Bridges, Walter, Bringmann, Kathrin
Format: Artikel
Sprache:eng
Schlagworte:
Circle method
False theta function
Jacobi form
Partition
Rank
Unimodal sequence
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Beschreibung
Zusammenfassung:We apply the new framework for modularity of false theta functions developed by the second author and Nazaroglu to study the asymptotic behavior of Taylor coefficients of false Jacobi forms. The examples we study generate moments of the rank for unimodal sequences. For two types of unimodal sequences, we prove asymptotic series for the rank moments.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.109074