On a class of elliptic functions associated with imaginary quadratic fields

Shen, Li-Chien

doi:10.1090/S0002-9939-03-07259-9

On a class of elliptic functions associated with imaginary quadratic fields
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Proc. Amer. Math. Soc. 132 (2004), 463-471 Request permission

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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