论文标题
大型算术进程和应用中的乘法功能
Multiplicative functions in large arithmetic progressions and applications
论文作者
论文摘要
我们为广泛的乘法算术功能建立了新的Bombieri-Vinogradov类型估计，并得出了多种应用，包括：Drappeau和Topacogullari最近估算的新证明； ERD {\ h o} S-Wintner类型的定理，其支持等于位于移位参数处的加法函数的级别集；以及迭代的对数定律，用于分布整数的主要因素，而整数因子加权$τ（n-1）$，其中$τ$表示除数函数。
We establish new Bombieri-Vinogradov type estimates for a wide class of multiplicative arithmetic functions and derive several applications, including: a new proof of a recent estimate by Drappeau and Topacogullari for arithmetical correlations; a theorem of Erd{\H o}s-Wintner type with support equal to the level set of an additive function at shifted argument; and a law of iterated logarithm for the distribution of prime factors of integers weighted by $τ(n-1)$ where $τ$ denotes the divisor function.
