# Warings problem for polynomials in two variables

Warings problem for polynomials in two variables - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Descargar gratis o leer online en formato PDF el libro: Warings problem for polynomials in two variables
We prove that all polynomials in several variables can be decomposed as the sums of $k$th powers: $Px 1, .,x n = Q 1x 1, .,x n^k+ .+ Q sx 1, .,x n^k$, provided that elements of the base field are themselves sums of $k$th powers. We also give bounds for the number of terms $s$ and the degree of the $Q i^k$. We then improve these bounds in the case of two variables polynomials of large degree to get a decomposition $Px,y = Q 1x,y^k+ .+ Q sx,y^k$ with $\deg Q i^k \le \deg P + k^3$ and $s$ that depends on $k$ and $\ln \deg P$.

Autor: Arnaud Bodin; Mireille Car

Fuente: https://archive.org/