Theta series associated with certain positive definite binary quadratic forms
Theta series associated with certain positive definite binary quadratic forms
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DOI：
10.4064/aa169-4-3
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发表时间：
2015
期刊：
影响因子：
0.7
通讯作者：
H. Chan;Pee Choon Toh
中科院分区：
文献类型：
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作者：
H. Chan;Pee Choon Toh
等价类的集合形成有限阿贝尔群C（d）。我们跟随D。Buell [3，p. 193]，并称d为恒等式判别式，如果C（d）是平凡群或2阶循环群的直和。判别式d是基本的，如果它不能写成st 2的形式，其中t > 1，并且s本身是判别式。共有101个已知的idoneal判别式，其中65个是基本的（见表1和表2）。巧合的是，在这101个idoneal判别式中，正好有65个判别式d（表2和表4），使得|D|/4是整数。这些整数统称为欧拉等元数
The set of equivalence classes forms a finite abelian group, C(d). We follow D. Buell [3, p. 193] and call d an idoneal discriminant if C(d) is the trivial group or a direct sum of cyclic groups of order 2. A discriminant d is fundamental if it cannot be written in the form st2 where t > 1 and s is itself a discriminant. There are a total of 101 known idoneal discriminants, 65 of which are fundamental (see Tables 1 and 2). Coincidentally, among these 101 idoneal discriminants, there are exactly 65 discriminants d (Tables 2 and 4) such that |d|/4 are integers. These integers are collectively known as Euler’s idoneal