Elliptic Curves with Complex Multiplication and a Character Sum
Elliptic Curves with Complex Multiplication and a Character Sum
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DOI：
10.1006/jnth.1996.0148
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发表时间：
1996-12
影响因子：
0.7
通讯作者：
R. Padma;S. Venkataraman
中科院分区：
文献类型：
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作者：
R. Padma;S. Venkataraman
摘要 设f(x)∈Q [X]是三次方，使得y2=f(x)是一条由[公式]、[公式]、[公式]或[公式]复数相乘的椭圆曲线。我们想要计算字符和[公式]，其中(·/p)是勒让德符号。我们证明计算有限数量的素数之和就足够了，而且这已经完成了。
Abstract Letf(x)∈ Q [X] be a cubic such thaty2=f(x) is an elliptic curve with complex multiplication by[formula],[formula],[formula]or[formula]. We want to calculate the character sum[formula]where (·/p) is the Legendre symbol. We show that it is enough to calculate the sum for a finite number of primes and this has been done.