On some cubic modular identities

Author:
Li-Chien Shen

Journal:
Proc. Amer. Math. Soc. **119** (1993), 203-208

MSC:
Primary 11F03

MathSciNet review:
1152291

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Abstract | References | Similar Articles | Additional Information

Abstract: Let and be the periods of . By evaluating the functional equations and at , we deduce a set of cubic modular identities from which the familiar modular equation of degree follows directly as a corollary.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1152291-6

Keywords:
Theta functions,
quadratic transformation,
modular identity

Article copyright:
© Copyright 1993
American Mathematical Society