Hilbert Class Polynomials and Traces of Singular Moduli
نویسندگان
چکیده
where q = e. The values of j(z) at imaginary quadratic arguments in the upper half of the complex plane are known as singular moduli. Singular moduli are algebraic integers which play prominent roles in classical and modern number theory (see [C, BCSH]). For example, Hilbert class fields of imaginary quadratic fields are generated by singular moduli. Furthermore, isomorphism classes of elliptic curves with complex multiplication are distinguished by singular moduli. Throughout, let d ≡ 0, 3 (mod 4) be a positive integer (so that −d is the discriminant of an order in an imaginary quadratic field), and let H(d) be the Hurwitz-Kronecker class number for the discriminant −d. Let Qd be the set of positive definite integral binary quadratic forms (note. including imprimitive forms, if there are any)
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