SOME NEW CANONICAL FORMS FOR POLYNOMIALS

被引：6

作者：

Reznick, Bruce ^{[1
,2
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Univ Illinois, Ctr Adv Study, Urbana, IL 61801 USA

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2013年 / 266卷 / 01期

关键词：

canonical forms; sums of powers of polynomials; WARING PROBLEM; THEOREM; SUMS;

D O I：

10.2140/pjm.2013.266.185

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give some new canonical representations for forms over C. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power of a linear form. A general cubic form in (x(1). . . , x(n)) can be written uniquely as a sum of the cubes of linear forms l(ij) (xi,. . . , x(j)), 1 <= i <= j <= n. A general ternary quartic form is the sum of the square of a quadratic form and three fourth powers of linear forms. The methods are classical and elementary.

引用

页码：185 / 220

页数：36

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