Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Modular Tranformations for Ramanujan's Tenth Order Mock Theta Functions

  • Received : 2004.02.23
  • Published : 2005.06.23
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Abstract

In this paper we obtain the transformations of the Ramanujan's tenth order mock theta functions under the modular group generators ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

Keywords

References

  1. Proc. Sympos. Pure Math. v.49 no.2 Mock theta functions Andrews, G.E.
  2. Adv. in Math. v.89 Ramanujan's 'Lost'Notebook VII: 'The sixth order mock theta functions Andrews, G.E.;Hickerson, D.
  3. A Brief Introduction to Theta Functions Bellman, R.E.
  4. Invent. Math. v.136 Tenth order mock theta functions in Ramanujan's 'Lost' Notebook Choi, Youn-Seo
  5. Basic Hypergeometric Series Gasper, G.;Rahman, M.
  6. The Ramanujan Journal v.7 Modular transformations of Ramanujan's fifth and seventh order Mock theta functions Gordon, B.;McIntosh, R.J.
  7. J. London Math. Soc. v.62 no.2 Some eight order Mock theta functions Gordon, B.;McIntosh, R.J.
  8. Collected Papers 1927 Ramanujan, S.
  9. The Lost Notebook and Other Unpublished Manuscripts Ramanujan, S.
  10. J. London Math. Soc. v.11 The final problem: An account of the Mock theta functions Watson, G.N.
  11. Proc. London Math. Soc. v.42 no.2 The Mock theta functions Watson, G.N.
  12. A Course of Modern Analysis Whittaker, E.T.;Watson, G.N.