In this paper,we study the linear independence between the distribution of the number of prime factors of integers and that of the largest prime factors of integers.Under a restriction on the largest prime factors of ...In this paper,we study the linear independence between the distribution of the number of prime factors of integers and that of the largest prime factors of integers.Under a restriction on the largest prime factors of integers,we will refine the Erdös–Kac Theorem and Loyd’s recent result on Bergelson and Richter’s dynamical generalizations of the Prime Number Theorem,respectively.At the end,we will show that the analogue of these results holds with respect to the Erdös–Pomerance Theorem as well.展开更多
基金supported by the National Natural Science Foundation of China(No.12288201)supported by the China Postdoctoral Science Foundation under grant number 2021TQ0350.
文摘In this paper,we study the linear independence between the distribution of the number of prime factors of integers and that of the largest prime factors of integers.Under a restriction on the largest prime factors of integers,we will refine the Erdös–Kac Theorem and Loyd’s recent result on Bergelson and Richter’s dynamical generalizations of the Prime Number Theorem,respectively.At the end,we will show that the analogue of these results holds with respect to the Erdös–Pomerance Theorem as well.
