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Terence Tao: The Erdős Discrepancy Problem

October 8, 2015
Presenters: Terence Tao
Length: 51 minutes 48 seconds

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Terence Tao - University of California, Los Angeles

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, Erdős 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 Erdős discrepancy problem was solved this September. In this talk I will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.

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