Tsz Ho Chan


Kennesaw State University

SCS Slide Set Variance of squarefull numbers in short intervals

"One central theme in number theory is the study of the distribution of prime numbers. For example, people are interested in large/small gaps between consecutive primes or how short an interval [x, x+h] contains a prime. Similar questions can be raised for other interesting number sequences such as sums of two squares, squarefree numbers, squarefull numbers, smooth numbers, .... Recently, Gorodetsky, Matom\"{a}ki, Radziwi\l{}\l{} and Rodgers did some breakthrough work concerning the variance of squarefree numbers in short intervals and arithmetic progressions. This prompted me to study the analogous questions for squarefull numbers (numbers like 72 = $2^3 3^2$ with exponents greater than one in its prime factorization). It is harder because squarefull numbers are much sparser than squarefree numbers."

I also have a preprint on the arXiv related to my slides. Its number is arXiv:2205.12108 .