English

Ramanujan's radial limits and mixed mock modular bilateral $q$-hypergeometric series

Number Theory 2016-12-09 v3

Abstract

Using results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsom, Ono, and Rhoades for mock theta functions. Here we see that the author's previous work on the dual nature of Appell--Lerch sums and partial theta functions and on constructing bilateral qq-series with mixed mock modular behaviour is well-suited for such radial limits. We present five more radial limit results which follow from mixed mock modular bilateral qq-hypergeometric series. We also obtain the mixed mock modular bilateral series for a universal mock theta function of Gordon and McIntosh. The later bilateral series can be used to compute radial limits for many classical second, sixth, eight, and tenth order mock theta functions.

Keywords

Cite

@article{arxiv.1309.4162,
  title  = {Ramanujan's radial limits and mixed mock modular bilateral $q$-hypergeometric series},
  author = {Eric Mortenson},
  journal= {arXiv preprint arXiv:1309.4162},
  year   = {2016}
}

Comments

To be published in the Proceedings of the Edinburgh Mathematical Society