ON THE NUMBER OF REPRESENTATIONS OF INTEGERS BY CERTAIN QUADRATIC FORMS
ON THE NUMBER OF REPRESENTATIONS OF INTEGERS BY CERTAIN QUADRATIC FORMS
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DOI：
10.1017/s0004972708000555
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发表时间：
2008-08
影响因子：
0.7
通讯作者：
S. Cooper
中科院分区：
文献类型：
--
作者：
S. Cooper
摘要利用生成函数导出正整数的二次型x12+x22+x32+2x42、x12+2x22+2x32 + 2x42、x12+x22+ 2x32+4x42和x12+2x22+4x32+4x42的表示数公式。这些公式表明，每种形式的表示数总是正数。文中还给出了一些涉及三角数和的类似结果。
Abstract Generating functions are used to derive formulas for the number of representations of a positive integer by each of the quadratic forms x12+x22+x32+2x42, x12+2x22+2x32+2x42, x12+x22+2x32+4x42 and x12+2x22+4x32+4x42. The formulas show that the number of representations by each form is always positive. Some of the analogous results involving sums of triangular numbers are also given.