Seminar: Kübra Benli - Sums of proper divisors with missing digits (Jan 14, 2026)

Speaker: Kübra Benli (Boğaziçi University)

Title: Sums of proper divisors with missing digits

Time: January 14, Wednesday, 2026 at 19:00 (Istanbul LT), 19:30 (Tehran LT), 21:30 (Allahabad LT)

Place: Online

Meeting ID: 997 1547 1656
Passcode: 848084

Abstract: 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 $\mathcal{A}$ is a set of integers with asymptotic density zero, then the preimage set $s^{-1}(\mathcal{A})$ also has asymptotic density zero. In this talk, we will discuss the verification of this conjecture when $\mathcal{A}$ is the set of integers with missing digits (also known as ellipsephic integers) by giving a quantitative estimate on the size of the set $s^{-1}(\mathcal{A})$. This talk is based on joint work with Giulia Cesana, C'{e}cile Dartyge, Charlotte Dombrowsky, Paul Pollack, and Lola Thompson.