Analytic prime number theory in the twenty-first century, Terence Tao,
8/7/2023, Warsaw - Numbers in the Universe school and conference.
Lecture 4. The Erdos discrepancy problem.
The discrepancy of a sequence f(1), f(2), ... of numbers is defined to be the largest value of |f(d) + f(2d) + ... + f(nd)| as n,d range over the natural numbers. In the 1930s, Erdos posed the question of whether any sequence consisting only of +1 and -1 could have bounded discrepancy. In 2010, the collaborative Polymath5 project showed (among other things) that the problem could be effectively reduced to a problem involving completely multiplicative sequences. Finally, using recent breakthroughs in the asymptotics of completely multiplicative sequences by Matomaki and Radziwill, as well as a surprising application of the Shannon entropy inequalities, the Erdos discrepancy problem was solved in 2015. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.
Course notes:
a.storyblok.com/f/240358/x/08...
Негізгі бет The Erdos discrepancy problem, Terence Tao, 4/4.
Пікірлер: 5