论文标题
关于Chowla猜想和离散傅立叶变换的注意
Note on the Chowla Conjecture and the Discrete Fourier Transform
论文作者
论文摘要
令$ x \ geq 1 $为一个大整数，让$ a_0 <a_1 <\ cdots <a_ {k-1} $为小的固定整数$ k $ -tuple，让$μ（n）\ in \ in \ { - 1,0,0,1 \} $是周期性的mobius函数。该注释表明，离散的傅立叶变换分析产生了周期性chowla猜想的简单解决方案。更准确地说，它导致形式的渐近公式$ \ sum_ {n \ leq x}μ（n+a_0）μ（n+a_1）\cdotsμ（n+a_ {k-1}）= o \ left（x（x（\ log x）^{ - c）
Let $x\geq 1$ be a large integer, and let $a_0<a_1<\cdots<a_{k-1}$ be a small fixed integer $k$-tuple, and let $μ(n)\in\{-1,0,1\}$ be the periodic Mobius function. This note shows that discrete Fourier transform analysis produces a simple solution of the periodic Chowla conjecture. More precisely, it leads to an asymptotic formula of the form $\sum_{n \leq x} μ(n+a_0) μ(n+a_1)\cdotsμ(n+a_{k-1}) =O\left( x(\log x)^{-c}\right)$, where $c>0$ is an arbitrary constant.
