Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions |
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Authors: | Gordon Basil Mcintosh Richard J |
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Institution: | (1) Department of Mathematics, University of California, Los Angeles, California, 90024;(2) Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada, S4S 0A2 |
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Abstract: | In his last letter to Hardy, Ramanujan defined 17 functions F(q), where |q| < 1. He called them mock theta functions, because as q radially approaches any point e
2 ir
(r rational), there is a theta function F
r(q) with F(q) – F
r(q) = O(1). In this paper we obtain the transformations of Ramanujan's fifth and seventh order mock theta functions under the modular group generators + 1 and –1/ , where q = e
i . The transformation formulas are more complex than those of ordinary theta functions. A definition of the order of a mock theta function is also given. |
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Keywords: | mock theta function modular form Mordell integral |
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