Modular Invariants Expressible in Terms of Quadratic and Cubic Irrationalities
Modular Invariants Expressible in Terms of Quadratic and Cubic Irrationalities
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用二次和三次无理数表示的模不变量
DOI：
10.1112/plms/s2-28.1.53
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发表时间：
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影响因子：
1.8
通讯作者：
W. E. H. Berwick
中科院分区：
文献类型：
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作者：
W. E. H. Berwick
54 WEH贝里克[May 12，and 7（0）3），etc.，是具有负判别式的不可约三次方程的共轭根。在所有这些情况下，j（to）和j（w）-1728在它们各自的域中被完全因式分解。j（to）和7（10）-1728的代数素因子的范数具有某些正则类型，在§ 10中指出。没有尝试已在此场合证明一般定理，关于这些素数的性质，这可能是从现在给出的结果。对于2、3、5、7、13阶变换的Klein主模 * T，当它与y（w）在同一数域中时，我们也注意到。
54 WEH BERWICK[May 12, and 7 (0) 3), etc., are conjugate roots of an irreducible cubic equation with negative discriminant. In all these cases j (to) and j (w)—1728 are here1 completely factorized in their respective fields. The norms of the algebraic prime factors of j (to) and 7 (10)—1728 are of certain regular types which are noted in § 10. No attempt has been made on this occasion toprove general theorems, regarding the nature of these primes, which might be conjectured from the results now given. Klein's principal modulus* T for transformations of orders 2, 3, 5, 7, 13 is also noted whenit lies in the same number-field as y (w).