Level 14 and 15 analogues of Ramanujan’s elliptic functions to alternative bases
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- by Shaun Cooper and Dongxi Ye PDF
- Trans. Amer. Math. Soc. 368 (2016), 7883-7910 Request permission
Abstract:
We briefly review Ramanujan’s theories of elliptic functions to alternative bases, describe their analogues for levels 5 and 7, and develop new theories for levels 14 and 15. This gives rise to a rich interplay between theta functions, eta-products and Eisenstein series. Transformation formulas of degrees five and seven for hypergeometric functions are obtained, and the paper ends with some series for $1/\pi$ similar to ones found by Ramanujan.References
Additional Information
- Shaun Cooper
- Affiliation: Institute of Natural and Mathematical Sciences, Massey University-Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand
- MR Author ID: 316980
- Email: s.cooper@massey.ac.nz
- Dongxi Ye
- Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
- MR Author ID: 1004870
- ORCID: 0000-0002-9986-388X
- Email: lawrencefrommath@gmail.com
- Received by editor(s): November 15, 2013
- Received by editor(s) in revised form: January 10, 2015
- Published electronically: November 16, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 7883-7910
- MSC (2010): Primary 11F11; Secondary 33C05
- DOI: https://doi.org/10.1090/tran6658
- MathSciNet review: 3546787