Number Theory Seminar

Average distribution of k-free numbers in arithmetic progressions

Speaker:  Kui Liu (Qingdao University, China)
Date:  Tuesday, 09 May 2023 - 12:30
Place:  Aula 520, Módulo 17, Departamento de Matemáticas, UAM


In this talk, we will first recall some previous results on the distribution of square-free and k-free numbers. Then we consider the distribution and average distribution of k -free numbers in arithmetic progressions. Finally, we will show how to estimate the average value of the error term of the asymptotic formula for the number of k -free numbers in arithmetic progressions. This is a joint work with I. E. Shparlinski and Tianping Zhang.