论文标题
三元二次形式代表相同的整数
Ternary quadratic forms representing same integers
论文作者
论文摘要
1997年，卡普兰斯基（Kaplansky）猜想，如果具有整数系数的两个积极确定的三元二次形式具有完全相同的积分表示，那么它们是等值的，无论是规则的还是三个三元二次形式的家族中的两家。在本文中，我们证明了代表不在Kaplansky列表中的相同整数的三元二次形式的存在。
In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isometric, both regular, or included either of two families of ternary quadratic forms. In this article, we prove the existence of pairs of ternary quadratic forms representing same integers which are not in the Kaplansky's list.
