Class Invariants from a New Kind of Weber-like Modular Equation
نویسنده
چکیده
A new technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely ‘algebraic’ method. They are obtained by means of specialising certain modular equations related to Weber’s modular equations of ‘irrational type’. The technique works for a large class of eta quotients evaluated at points in an imaginary quadratic field with discriminant d ≡ 1 (mod 8). In particular, this method does place any restriction on the class number of the associated imaginary quadratic number field.
منابع مشابه
A New Class of Modular Equation for Weber Functions
We describe the construction of a new type of modular equation for Weber functions. These bear some relationship to Weber’s modular equations of irrational kind. Numerous examples of these equations are explicitly computed. We also obtain some modular equations of irrational kind which Weber was not able to compute.
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