The Selberg-Delange method in short intervals with some applications

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（3）
• 页码范围: 447-468
• 页数: 22页
• 语种: 英文

摘要

In this paper,we establish a quite general mean value result of arithmetic functions over short intervals with the Selberg-Delange method and give some applications.In particular,we generalize Selberg's result on the distribution of integers with a given number of prime factors and Deshouillers-Dress-Tenenbaum's arcsin law on divisors to the short interval case.