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由Siegel公式导出一个整数表为8个平方数之和的表示数

Keywords: Siegel公式,二次型,Jacobi八平方和公式

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Abstract:

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.

References

[1]  Hardy G H, Wright E M. 数论导引[M]. 5版. 张明尧,张凡,译. 北京:人民邮电出版社,2008:334.
[2]  Hanke J. Quadratic forms and automorphic forms[OL]. arXiv:1105.5759,2012.
[3]  Ireland K, Rosen M. A Classical Introduction to Modern Number Theory[M]. 2nd ed. New York:Springer-Verlag,1990:103.
[4]  Tan Q R, Luo M, Lin Z B. Determinants and divisibility of power GCD and power LCM matrices on finitely many coprime divisor chains[J]. Appl Math Comput,2013,219:8112-8120.
[5]  Tan Q R. Divisibility among power GCD matrices and among power LCM matrices on finitely many coprime divisor chains[J]. Linear Algebra and Its Applications,2013,438:1454-1466.
[6]  Tan Q R, Lin Z B, Liu L. Divisibility among power GCD matrices and among power LCM matrices on two coprime divisor chains II[J]. Linear and Multilinear Algebra,2011,59:969-983.
[7]  Bateman P T. On the representations of a number as the sum of three squares[J]. Trans Amer Math Soc,1951,71:70-101.
[8]  Cooper S. Sums of five, seven and nine squares[J]. Ramanujan J,2002,6:469-490.
[9]  Cooper S, Hirschhorn M D. On the number of primitive representations of integers as sums of squares[J]. Ramanujan J,2007,13:7-25.
[10]  Lin J F. The number of representations of an integeras a sum of eight squares[J]. Northeastern Math J,2002,18(1):19-20.
[11]  Grosswald E. Representations of Integers as Sums of Squares[M]. New York:Springer-Verlag,1985.
[12]  Hirschhorn M D. A simple proof of Jacobi’s four square theorem[J]. Proc Amer Math Soc,1987,101:436-438.
[13]  Mordell L J. On the representation of numbers as the sum of 2r squares[J]. Quart J Pure Appl Math,1917,48:93-104.
[14]  Olds C D. On the number of representations of the square of an integer as the sum of three squares[J]. Amer J Math,1941,63:763-767.
[15]  Glaisher J W L. On the numbers of representations of a number as a sum of 2r squares, where 2r does not exceed eighteen[J]. Proc London Math Soc,1907,5:479-490.
[16]  Ewell J A. On sums of sixteen squares[J]. Rocky Mountain J Math,1987,17:295-299.

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