论文标题
有关Weyl等级定理的注释
A Note about Weyl Equidistribution Theorem
论文作者
论文摘要
H. Weyl在\ cite {weyl}中证明了多项式的整数评估。我们使用Weyl的结果证明了这一事实的更高维度类似物。也就是说，我们证明，每当至少一种非无的系数是不合理的，对晶格点的多项式评估是等分分配的mod 1。这一结果强调了\ cite {polweyl}中Arhipov-karacuba-čubarikov的主要结果。我们证明了这种类似物作为定理的推论，该定理保证了对晶格评估1的等分分配模式1，以满足其对衍生物的某些限制的所有功能。我们证明的另一个推论是，对于$ p \ in（1，\ infty）$，整数矢量的$ \ ell^p $ norms narms quardistribed mod 1。
H. Weyl proved in \cite{Weyl} that integer evaluations of polynomials are equidistributed mod 1 whenever at least one of the non-free coefficients is irrational. We use Weyl's result to prove a higher dimensional analogue of this fact. Namely, we prove that evaluations of polynomials on lattice points are equidistributed mod 1 whenever at least one of the non-free coefficients is irrational. This result strengths the main result of Arhipov-Karacuba-Čubarikov in \cite{PolWeyl}. We prove this analogue as a Corollary of a Theorem that guarantees equidistribution of lattice evaluations mod 1 for all functions which satisfy some restrains on their derivatives. Another Corollary we prove is that for $p\in(1,\infty)$ the $\ell^p$ norms of integer vectors are equidistributed mod 1.
