Generalised Weber Functions
نویسندگان
چکیده
A generalisedWeber function is wN (z) = η(z/N)/η(z) where η(z) is the Dedekind function and N is any integer (the original function corresponds to N = 2). We give the complete classification of cases where some power w N evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the relevant modular equation relating wN (z) and j(z).
منابع مشابه
Generalised Weber Functions. I
A generalised Weber function is given by wN (z) = η(z/N)/η(z), where η(z) is the Dedekind function and N is any integer; the original function corresponds to N = 2. We classify the cases where some power w N evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formu...
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