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Transactions of the American Mathematical Society

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Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook


Authors: Bruce C. Berndt, Sen-Shan Huang, Jaebum Sohn and Seung Hwan Son
Journal: Trans. Amer. Math. Soc. 352 (2000), 2157-2177
MSC (2000): Primary 35Dxx; Secondary 11B65, 11A55, 30B70
DOI: https://doi.org/10.1090/S0002-9947-00-02337-0
Published electronically: February 8, 2000
MathSciNet review: 1615939
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Abstract:

In his first two letters to G. H. Hardy and in his notebooks, Ramanujan recorded many theorems about the Rogers-Ramanujan continued fraction. In his lost notebook, he offered several further assertions. The purpose of this paper is to provide proofs for many of the claims about the Rogers-Ramanujan and generalized Rogers-Ramanujan continued fractions found in the lost notebook. These theorems involve, among other things, modular equations, transformations, zeros, and class invariants.


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Additional Information

Bruce C. Berndt
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: berndt@math.uiuc.edu

Sen-Shan Huang
Affiliation: Department of Mathematics, National Chang Hua University of Education, Chang Hua City, Taiwan, Republic of China
Email: shuang@math.ncue.edu.tw

Jaebum Sohn
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: j-sohn@math.uiuc.edu

Seung Hwan Son
Affiliation: 1808 Stearns Hill Road, Waltham, Massachusetts 02451-3338
Email: son@ptc.com

DOI: https://doi.org/10.1090/S0002-9947-00-02337-0
Received by editor(s): September 16, 1997
Received by editor(s) in revised form: March 3, 1998
Published electronically: February 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society