6 papers
Asymptotic uncorrelations between functions with squarefull kernel and functions of invariant average
Xiang Su, Biao Wang, Shaoyun Yi
In 1986, Ivić and Tenenbaum introduced arithmetic functions with squarefull kernel, which are also called -functions. Later, Erdős and Ivić gave an asymptotic estimate on the sh…
The prime number theorem over integers of power-free polynomial values
Biao Wang, Shaoyun Yi
Let be an irreducible polynomial of degree . Let be an integer. The number of integers such that is -free is widely studied in…
On averages of completely multiplicative functions over co-prime integer pairs
Biao Wang
Recently, Donoso, Le, Moreira and Sun studied the asymptotic behavior of the averages of completely multiplicative functions over the Gaussian integers. They derived Wirsing's theo…
Some ergodic theorems over -full numbers
Biao Wang
In 2022, Bergelson and Richter established a new dynamical generalization of the prime number theorem. Later, Loyd showed a disjoint form with the ErdÅs-Kac theorem. Recently, the…
Some ergodic theorems over squarefree numbers and squarefull numbers
Huixi Li, Biao Wang, Chunlin Wang +1
In 2022, Bergelson and Richter gave a new dynamical generalization of the prime number theorem by establishing an ergodic theorem along the number of prime factors of integers. The…
A logarithmic analogue of Alladi's formula
Biao Wang
Let be the Möbius function. Let denote the smallest prime factor of an integer . In 1977, Alladi established the following formula related to the prime number…