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
设K是有理数域的二次代数扩张,aK(n)是K上的理想计数函数,本文利用Selberg-Delange方法给出aK(n)l在短区间n∈[x,x+y]上的均值估计如下:对于一致成立,其中c,c1,c2均为与l有关的常数。Let K be a quadratic algebraic extension of , aK(...设K是有理数域的二次代数扩张,aK(n)是K上的理想计数函数,本文利用Selberg-Delange方法给出aK(n)l在短区间n∈[x,x+y]上的均值估计如下:对于一致成立,其中c,c1,c2均为与l有关的常数。Let K be a quadratic algebraic extension of , aK(n) is an ideal counting function on K. In this paper, we use the Selberg-Delange method to give the mean estimation of aK(n)l in a short interval as follows: It is consistent for where c,c1,c2 are constants related to l.展开更多
We study the Cesaro means related to the divisor function. We show that the DDT Theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and ...We study the Cesaro means related to the divisor function. We show that the DDT Theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and by Cui-Wu.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.
文摘设K是有理数域的二次代数扩张,aK(n)是K上的理想计数函数,本文利用Selberg-Delange方法给出aK(n)l在短区间n∈[x,x+y]上的均值估计如下:对于一致成立,其中c,c1,c2均为与l有关的常数。Let K be a quadratic algebraic extension of , aK(n) is an ideal counting function on K. In this paper, we use the Selberg-Delange method to give the mean estimation of aK(n)l in a short interval as follows: It is consistent for where c,c1,c2 are constants related to l.
基金Acknowledgements The authors are indebted to the anonymous referees for valuable suggestions, which led to Lemma 2 in its present shape. The first author is especially grateful to his supervisor, Prof. Hongze Li, for his unending encouragement and his effort that provides the opportunities to communicate with foreign specialists. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11271249） and the Specialized Research Fund for the Doctoral Program of Higher Education （Grant No. 20120073110059）.
文摘We study the Cesaro means related to the divisor function. We show that the DDT Theorem holds over square-free numbers in short interval, which generalizes some results established by Deshouillers-Dress-Tenenbaum and by Cui-Wu.
