Khalid Younis

Smooth numbers and digit constraints

A popular topic in number theory is to investigate sequences of arithmetic interest after imposing some constraint on their digits. For example, one can arbitrarily prescribe a small fraction of digits, which simultaneously generalises the problem of counting elements in short intervals and in arithmetic progressions. We will discuss the roles of harmonic analysis and zeros of L-functions, with a focus on recent work on smooth numbers, that is, numbers whose prime factors are all small.