论文标题
一些算术功能的谐波分析
Harmonic Analysis of some arithmetical functions
论文作者
论文摘要
我们研究了三个功能，即变量$ z $，DIRICHLET系列中的功率系列，并在变量$ s $中以及由算术函数给出的系数。一个重要的观点是将这些功能与某些希尔伯特空间联系起来。使用了三种主要成分：Davenport对Möbius函数总和的估计，这是算术算术卷议案的lucht的结果，并引入了Power系列上的操作$ \ otimes $，自然与上述希尔伯特空间有关。
We study three functions which are power series in the variable $z$, Dirichlet series in the variable $s$ and with coefficients given by arithmetical functions. A strong point is to relate these functions to some Hilbert spaces. Three main ingredients are used: an estimate of Davenport on sums of Möbius functions, a result of Lucht on convolutions of arithmetical Dirichlet series and the introduction of an operation $\otimes$ on power series, naturally associated with the mentioned Hilbert spaces.
