On the Waring problem for polynomial rings.
نویسندگان
چکیده
In this note we discuss an analog of the classical Waring problem for C[x0,x1,...,x(n)]. Namely, we show that a general homogeneous polynomial p ∈ C[x0,x1,...,x(n)] of degree divisible by k≥2 can be represented as a sum of at most k(n) k-th powers of homogeneous polynomials in C[x0,x1,...,x(n)]. Noticeably, k(n) coincides with the number obtained by naive dimension count.
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ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 109 15 شماره
صفحات -
تاریخ انتشار 2012