Singular values of the Rogers-Ramanujan continued fraction |
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| Authors: | Alice Gee Mascha Honsbeek |
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| Institution: | (1) Quantitative Risk Analytics, ABN AMRO Bank, P.O. Box 283 (HQ 9051), 1000 EA Amsterdam, The Netherlands;(2) Faculteit der Wiskunde en Informatica, Katholieke Universiteit Nijmegen, Postbus 9010, 6500 GL Nijmegen, The Netherlands |
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| Abstract: | Let z∊ C be imaginary quadratic in the upper half plane. Then the Rogers-Ramanujan continued fraction evaluated at q = e 2π iz is contained in a class field of Q(z). Ramanujan showed that for certain values of z, one can write these continued fractions as nested radicals. We use the Shimura reciprocity law to obtain such nested radicals
whenever z is imaginary quadratic.
2000 Mathematics Subject Classification Primary—11Y65; Secondary—11Y40 |
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| Keywords: | Rogers-Ramanujan continued fraction Shimura reciprocity |
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