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 \(N=1,2,3,4\).
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We would like to thank O. Warnaar for helpful comments and suggestions.
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This research was supported byMinistry of Science and Higher Education of the Russian Federation, agreement No. 075-15-2019-1619.
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Mortenson, E.T. On Hecke-type double-sums and general string functions for the affine Lie algebra \(A_{1}^{(1)}\). Ramanujan J 63, 553–582 (2024). https://doi.org/10.1007/s11139-023-00737-x
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DOI: https://doi.org/10.1007/s11139-023-00737-x