论文标题
算术进程中广义除数函数方差的下限
A lower bound for the variance of generalized divisor functions in arithmetic progressions
论文作者
论文摘要
我们证明，对于大量的乘法函数（称为广义除数函数），可以找到算术进程中相应方差的下限。作为主要的推论，我们推断出任何$α$倍的除数函数的结果，即使考虑到一系列参数$α$，即使在\ {1 \} \ cup- {1 \} \ cup- \ cup- \ mathbb {n} $中，$α\ not \我们的作品建立在Harper和Soundararajan的基础上，他们处理了$ k $ - 折叠函数的特定情况$ d_k（n）$，并带有$ k \ in \ mathbb {n} _ {\ geq 2} $。
We prove that for a large class of multiplicative functions, referred to as generalized divisor functions, it is possible to find a lower bound for the corresponding variance in arithmetic progressions. As a main corollary, we deduce such a result for any $α$-fold divisor function, for any complex number $α\not\in \{1\}\cup-\mathbb{N}$, even when considering a sequence of parameters $α$ close in a proper way to $1$. Our work builds on that of Harper and Soundararajan, who handled the particular case of $k$-fold divisor functions $d_k(n)$, with $k\in\mathbb{N}_{\geq 2}$.
