On Hecke-type double-sums and general string functions for the affine Lie algebra $A_1^{(1)}$

Abstract

We demonstrate how formulas that express Hecke-type double-sums in terms of theta functions and Appell--Lerch functions -- the building blocks of Ramanujan's mock theta functions -- can be used to give general string function formulas for the affine Lie algebra $A_1^{(1)}$ for levels $N=1,2,3,4$.

27 pages. arXiv admin note: text overlap with arXiv:2107.06225

References in corpus (2)

• Mock Theta Functions
• On string functions and double-sum formulas

Cited by in corpus (1)

• Two $2/5$-level mock theta conjecture-like identities