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Список литературы
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Andrews G. E., Hickerson D. R., “Ramanujan's “lost” notebook. VII. The sixth order mock theta functions”, Adv. Math., 89:1 (1991), 60–105 |
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Andrews G. E., Warnaar S. O., “The Bailey transform and false theta functions”, Ramanujan J., 14:1 (2007), 173–188 |
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Chan S. H., Kim B., “On some double-sum false theta series”, J. Number Theory, 190 (2018), 40–55 |
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Kim B., Lovejoy J., “Partial indefinite theta identities”, J. Aust. Math. Soc., 102:2 (2017), 255–289 |
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Habiro K., “A unified Witten–Reshetikhin–Turaev invariant for integral homology spheres”, Invent. Math., 171:1 (2008), 1–81 |
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Hickerson D. R., Mortenson E. T., “Hecke-type double sums, Appell–Lerch sums, and mock theta functions. I”, Proc. Lond. Math. Soc. (3), 109:2 (2014), 382–422 |
8. |
K. Hikami, “Hecke type formula for unified Witten–Reshetikhin–Turaev invariants of higher-order mock theta functions”, Int. Math. Res. Not. IMRN, 2007, no. 7, rnm 022, 32 pp. |
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Hikami K., Lovejoy J., “Torus knots and quantum modular forms”, Res. Math. Sci., 2 (2015), 2, 15 pp. |
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Matsusaka T., Hikami's observations on unified WRT invariants and false theta functions, arXiv: 2212.06337 |
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Mortenson E. T., “Ramanujan's $_{1}\psi_1$ summation, Hecke-type double sums, and Appell–Lerch sums”, Ramanjuan J., 29:1-3 (2012), 121–133 |
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Mortenson E. T., “On the dual nature of partial theta functions and Appell–Lerch sums”, Adv. Math., 264 (2014), 236–260 |
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Mortenson E. T., “A double-sum Kronecker-type identity”, Adv. in Appl. Math., 82 (2017), 155–177 |
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Mortenson E. T., “A heuristic guide to evaluating triple-sums”, Hardy–Ramanujan J., 43 (2020), 99–121 |
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Mortenson E. T., “Hecke–Rogers double-sums and false theta functions”, Res. Number Theory, 7:2 (2021), 28, 20 pp. |
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Murakami Y., Witten–Reshetikhin–Turaev invariants and indefinite false theta functions for plumbing indefinite H-graphs, arXiv: 2212.09972v1 |
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Mortenson E. T., Zwegers S., “The mixed mock modularity of certain duals of generalized quantum modular forms of Hikami and Lovejoy”, Adv. Math., 418 (2023), 108944, 27 pp. |
19. |
Ramanujan S., The lost notebook and other unpublished papers, Springer-Verlag, Berlin; Narosa Publ. House, New Delhi, 1988 |
20. |
Zwegers S. P., Mock theta functions, Ph.D. Thesis, Univ. Utrecht, 2002 |