UBC Number Theory Seminar: Kübra Benli

Let s(n) denote the sum of proper divisors of a positive integer n. In 1992, Erd\H{o}s, Granville, Pomerance, and Spiro conjectured that if  is a set of integers with asymptotic density zero then the preimage set s−1() also has asymptotic density zero. In this talk, we will discuss the verification of this conjecture when  is the set of integers with missing digits (also known as ellipsephic integers) by giving a quantitative estimate on the size of the set s−1(). This talk is based on the joint work with Giulia Cesana, C\'{e}cile Dartyge, Charlotte Dombrowsky and Lola Thompson.