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 ...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.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11671253, 11771252 and 11531008)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20120073110059)+1 种基金Program for Innovative Research Team in University of Ministry of Education of China (Grant No. IRT16R43)Taishan Scholars Project, the Program PRC 1457-AuForDiP (CNRS-NSFC)
文摘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.
