特殊数在算术级数上的分布
The Distribution of Special Numbers in Arithmetic Progressions
王南翔 1戴浩波1
作者信息
摘要
设正整数n的素数分解为n＝p1a1p2a2...pkak,ai＞0.若所有的ai均不相同,那么称n为特殊数.特殊数是近几年提出的新概念,Aktas Kevser和Murty Ram计算了特殊数个数的渐进公式.利用Siegel-Walfisz定理、Abel求和等一系列工具可以解决特殊数在算数级数上的分布,并且在广义黎曼假设的基础上,可以缩小对模q的限制.在此基础上,未来可解决特殊数的Titchmarsh除数函数问题.
Abstract
Let n=p1a1p2a2...pkak be the canonical prime factorization of n,ai＞0.Then n is a special number if all the ai are distinct.The concept of the special number is newly put forward in these years.Aktas Kevser and Murty Ram compute the number of special numbers.By using a series of tools such as the Siegel-Walfisz Theorem and Abel summation,one can solve the distribution of the special numbers in arithmetic progressions,and by using GRH,one can reduce restrictions of modq,and,based on the above,one can solve the Titchmarsh divisor problem for the special numbers in the future.
关键词
特殊数/Siegel-Walfisz定理/Brun-Titchmarsh不等式/广义黎曼假设Key words
special number/Siegel-Walfisz Theorem/Brun-Titchmarsh Inequality/Generalized Riemann Hypothesis引用本文复制引用
出版年
2024
NETL
NSTL
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