论文标题
legendre-teege互惠
Legendre-Teege Reciprocity
论文作者
论文摘要
Legendre发表了第一次尝试证明二次互惠定律。但是，以其最终形式（1797年）有一个差距。大约125年后，赫尔曼·特吉（Herman Teege）发表了第一个严格的证据，证明未经证实的假设形成了这一差距。然后，48年后，肯尼思·罗杰斯（Kenneth Rogers）发表了第二个（但隐性）的证据。这些证据使Legendre的尝试列出了完整的证据。文献中没有出现这些证据的详细说明。我们的纸张填补了这一空白。
Legendre published the first attempted proof of the law of Quadratic Reciprocity. But, in its final form (1797), it had a gap. Some 125 years later Herman Teege published the first rigorous proof of the unproven hypothesis which formed that gap. Then, 48 years later Kenneth Rogers published a second (but implicit) proof. These proofs lifted Legendre's attempt to the list of complete proofs. No detailed exposition of these proofs appears in the literature. Our paper fills that gap.
