Number Theory Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Literature, Cultures, and Linguistics Building, Room G-32
- Date
- Nov 14, 2023 11:00 - 11:50 am
- Speaker
- Dimitris Koukoulopoulos (Université de Montréal)
- Contact
- Jesse Thorner and Yuan Liu
- jat9@illinois.edu and yyyliu@illinois.edu
- Views
- 40
- Originating Calendar
- Number Theory Seminar Calendar
Title: The mean value of the Erd\H os--Hooley Delta function
Abstract: The Erd\H os--Hooley Delta function is defined for $n\in\mathbb{N}$ as $\Delta(n)=\sup_{u\in\mathbb{R}} \#\{d|n : e^u<d\le e^{u+1}\}$. In a seminal 1979 paper, Hooley proved that estimates of its mean value can be exploited to count solutions to certain Diophantine equations. In this talk, I will present recent work, joint with Kevin Ford and Terence Tao, that establishes improved upper and lower bounds on the mean value of Delta.