Hecke-type double sums and mock theta functions
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 191-215
MSC: Primary 33D15; Secondary 11F27.
DOI: 10.4064/cm8886-10-2022
Published online: 2 January 2023
Abstract
Mock theta functions were first introduced by Ramanujan in his last letter to Hardy. In the literature, Hecke-type double sums for the classical mock theta functions play an important role in proving mock theta conjectures. In this paper, with the aid of some $q$-series identities, we establish Hecke-type double sums for some new mock theta functions. All the Hecke-type double sums are represented in the form of $f_{a,b,c}(x,y,q)$ which is defined by Hickerson and Mortenson. Moreover, we express these functions in terms of Appell–Lerch sums and theta functions.
