Following the method of Seifert surfaces in knot theory, we define arithmetic linking numbers and height pairings of ideals using arithmetic duality theorems, and compute them in terms of n-th power residue symbols. This formalism leads to a precise arithmetic analogue of a 'path-integral formula' for linking numbers.

中文翻译：

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阿贝尔算术陈-西蒙斯理论和算术关联数

遵循结理论中的Seifert曲面方法，我们使用算术对偶定理定义了理想的算术链接数和高度对，并根据n次方残差符号计算它们。这种形式主义导致了用于链接数字的“路径积分公式”的精确算术模拟。