论文标题
K-forunous功能的均匀力量总和
Sums of even powers of k-regulous functions
论文作者
论文摘要
我们提供了$ \ mathbb {r}^n $在$ k \ geq 1 $和$ n \ geq 2 $上的非负$ k $ gogulous函数的示例，该功能无法写成$ k $ oggogulous函数的平方之和。然后，我们获得了pythagoras编号的下限$ p_ {2d}（\ Mathcal {r}^k（\ Mathbb {r}^n））$ $ k $ - $ k $的$ gogulo form-for $ \ mathbb {r}^n $ for $ k \ geq 1 $和$ n \ geq geq 2 $。我们还证明，$ 0 $ 0 $的圆环的第二个pythagoras编号$ \ MATHCAL {r}^0（x）$在不可约$ 0 $ 0 $ 0 $ -Roggual的仿射品种$ x $是有限的，并从上面界限$ 2^{\ dim x} $。
We provide an example of a nonnegative $k$-regulous function on $\mathbb{R}^n$ for $k\geq 1$ and $n \geq 2$ which cannot be written as a sum of squares of $k$-regulous functions. We then obtain lower bounds for Pythagoras numbers $p_{2d}(\mathcal{R}^k(\mathbb{R}^n))$ of $k$-regulous functions on $\mathbb{R}^n$ for $k\geq 1$ and $n\geq 2$. We also prove that the second Pythagoras number of the ring of $0$-regulous functions $\mathcal{R}^0(X)$ on an irreducible $0$-regulous affine variety $X$ is finite and bounded from above by $2^{\dim X}$.
