论文标题
对具有单二型系数的复杂多项式的Sidon常数的估计值
An estimate of Sidon constant for complex polynomials with unimodular coefficients
论文作者
论文摘要
在本文中，我们关注的是某些有界程度但大量变量的多项式的hillust-hille型不平等现象。由于多项式将在组上定义，因此可以将问题视为Sidon常数的估计。在大多数情况下，锋利的常数是未知的。我们估计有关$ n $变量的$ d $多项式的Sidon类型估计的通用常数，$ n $ z_1，\ dots，z_n $，具有单对数系数。对于具有系数绝对值的多项式，这使我们能够从\ cite {dgms}提高估计值。主要结果是下面的定理1.7。
In this paper we are concerned with the Bohnenblust--Hille type inequalities for certain polynomials of bounded degree but of very large number of variables. As the polynomials will be defined on groups, one can think about the problem as the estimate of Sidon constants. In most cases the sharp constants are unknown. We estimate the universal constant concerning the Sidon type estimates of degree $d$ polynomials of $n$ variables $z_1, \dots, z_n$ with unimodular coefficients. For polynomials that have constant absolute value of coefficients, this allows us to improve the estimate from \cite{DGMS}. The main result is Theorem 1.7 below.
