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Article Dans Une Revue Hardy-Ramanujan Journal Année : 2023

The mixed mock modularity of a new $U$-type function related to the Andrews-Gordon identities

Résumé

In this paper we resolve a question by Bringmann, Lovejoy, and Rolen on a new vector-valued $U$-type function. We obtain an expression for a corresponding family of Hecke--Appell-type sums in terms of mixed mock modular forms; that is, we express the sum in terms of Appell functions and theta functions. This $U$-type function appears from considering the special polynomials related to generating functions for the partitions occurring in Gordon’s generalization of the Rogers--Ramanujan identities.
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Dates et versions

hal-03914253 , version 1 (28-12-2022)

Identifiants

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Nikolay E Borozenets. The mixed mock modularity of a new $U$-type function related to the Andrews-Gordon identities. Hardy-Ramanujan Journal, 2023, Volume 45 - 2022, pp.108 -- 129. ⟨10.46298/hrj.2023.10911⟩. ⟨hal-03914253⟩
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