🔖 The ErdŇĎs Discrepancy Problem (6.09.2017) | Terence Tao | YouTube

Bookmarked The ErdŇĎs Discrepancy Problem (6.09.2017) at Instytut Matematyczny Uniwersytetu WrocŇāawskiego by Terence TaoTerence Tao (YouTube)

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 and d range over the natural numbers. In the 1930s, ErdŇĎs 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 RadziwiŇāŇā, as well as a surprising application of the Shannon entropy inequalities, the ErdŇĎs discrepancy problem was solved in 2015. In his talk TT will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.

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