zbMATH — the first resource for mathematics

Hecke modular form expansions for eighth order Mock theta functions. (English) Zbl 1089.33014
The notion of a mock theta function goes back to Ramanujan. Since then various mock theta functions of different order have been found by several authors. The order of a mock theta function is analogous to the level of a modular form. In this paper the author uses Bailey pair method to derive Hecke type modular series for the eighth order mock theta functions. By using these Hecke type series, he gives a relation between the eighth order mock theta functions \(S_{0}(q)\), \(S_{1}(q)\) and theta functions.

33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
11F11 Holomorphic modular forms of integral weight
11F27 Theta series; Weil representation; theta correspondences
Full Text: DOI
[1] G. E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc. 293 (1986), 113-134. · Zbl 0593.10018
[2] G. E. Andrews and D. Hickerson, Ramanujan’s “Lost” Notebook VII: The sixth order mock theta functions, Adv. in Math. 89 (1991), 60-105. · Zbl 0739.11042
[3] Youn-Seo Choi, Tenth order mock theta functions in Ramanujan’s “Lost” Notebook, Invent. Math. 136 (1999), 497-569. · Zbl 0951.33013
[4] B. Gordon and R. J. McIntosh, Some eight order Mock theta functions, J. London Math. Soc. (2) 62 (2000), 321-335. · Zbl 1031.11007
[5] G. Gasper and M. Rahman, Basic Hypergeometric Series , Cambridge University Press, Cambridge (1990). · Zbl 0695.33001
[6] D. Hickerson, A proof of mock theta conjectures, Invent. Math. 94 (1998), 639-660. · Zbl 0661.10059
[7] S. Ramanujan, The “Lost” Notebook and other unpublished papers New Delhi , Narosa Publishing House (1988). · Zbl 0639.01023
[8] B. Srivastava, Application of Constant term method to Ramanujan’s mock theta functions, Submitted for publication. · Zbl 1257.11041
[9] G. N. Watson, The final problem: An account of the mock theta functions, J. London Math. Soc. 11 (1936), 55-80. · Zbl 0013.11502
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.