论文标题
一类乘函数的一类差异的差异
The variance of a general class of multiplicative functions in short intervals
论文作者
论文摘要
我们通过将“短平均值”与其“长平均值”相关联，研究一般的乘法功能。更准确地说，我们渐近地估算了此类函数在短时间间隔的差异，并使用傅立叶分析和对某些二进制形式的合理点进行计数。 我们的结果适用于有趣的乘法函数$μ_k（n），\ frac {ϕ（n）} {n}，\ frac {n} {n} {ϕ（n）}，$ $μ^2（n） $（-1）^{\＃\ {p \，：\，p^k | n \}} $以及许多其他人在文献中以短期间隔建立各种新结果和改进。
We study a general class of multiplicative functions by relating "short averages" to its "long average". More precisely, we estimate asymptotically the variance of such a class of functions in short intervals using Fourier analysis and counting rational points on certain binary forms. Our result is applicable to the interesting multiplicative functions $μ_k(n),\frac{ϕ(n)}{n}, \frac{n}{ϕ(n)},$ $μ^2(n)\frac{ϕ(n)}{n}$, $σ_α(n)$, $(-1)^{\#\{p\,: \, p^k|n\}}$ and many others that establish various new results and improvements in short intervals to the literature.
