Hilbert class polynomials and traces of singular moduli
Hilbert class polynomials and traces of singular moduli
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希尔伯特类多项式和奇异模量的迹
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
K. Ono
中科院分区：
文献类型：
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作者：
J. Bruinier;P. Jenkins;K. Ono
其中q = e。在复平面上半部分的虚二次变元处的j（z）的值被称为奇异模。奇异模是在古典和现代数论中扮演重要角色的代数整数（见[C，BCSH]）。例如，虚二次域的Hilbert类域由奇异模生成。此外，利用奇异模来区分具有复数乘法的椭圆曲线的同构类。在整个过程中，令d <$0，3（mod 4）是一个正整数（因此−d是虚二次域中一个阶的判别式），令H（d）是判别式−d的Hurwitz-Kronecker类数。设Qd是正定积分二元二次型的集合（注。包括非原始形式，如果有的话）
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)