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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a class of elliptic functions associated with imaginary quadratic fields


Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 132 (2004), 463-471
MSC (2000): Primary 33E05
Published electronically: August 28, 2003
MathSciNet review: 2022370
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Abstract: Let $-D$ be the field discriminant of an imaginary quadratic field. We construct a class of elliptic functions associated naturally with the quadratic field $Q(\sqrt {-D})$ which, combined with the general theory of elliptic functions, allows us to provide a unified theory for two fundamental results (one classical and one due to Ramanujan) about the elliptic functions.


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Additional Information

Li-Chien Shen
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611-2082
Email: shen@math.ufl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07259-9
PII: S 0002-9939(03)07259-9
Keywords: Elliptic function, character, class number, quadratic field, discriminant
Received by editor(s): October 3, 2002
Published electronically: August 28, 2003
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2003 American Mathematical Society