Régis de la Bretèche: Mean value of Erdos–Hooley Delta-function

Speaker
Régis de la Bretèche,Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris Cité

Abstract
The Erdos–Hooley Delta-function is a measure of divisors concentration in a dyadic interval of an integer. Recently, Ford, Koukoulopoulos and Tao proved new upper and lower bound of the mean value of Erdos–Hooley Delta-function. In a joint work with Tenenbaum, we improve their result. We shall explain the new ideas of Ford—Koukoulopoulos—Tao and how to improve their results. We will present some applications in diophantine geometry.