由Siegel公式导出一个整数表为8个平方数之和的表示数

The Representation Number of an Integer as a Sum of Eight Squares by Using Siegel's Formula

特定的数,将其表示为8个平方数的和的表示方法有多少种?对于这个问题,有多种不同的解决方式,不过绝大多数结果都是利用由椭圆函数理论推导出的Jacobi公式的演绎结论.通过非椭圆函数理论的一种新途径,利用二次型的解析理论中的Siegel公式给出Jacobi八平方和公式的一个新证明.

How many way we can represent certain numbers as a sum of eight squares？ This question can be treated in many differ- ent way, but the most definitive result is the following exact formula of Jaeobi which he derived via the theory of elliptic functions. In this paper, we give a proof of Jacobi＇ s eight squares thorem in new way by using Siegel＇ s formula in the analytic theory of quadratic forms, not through the theory of elliptic functions.