Joni Teräväinen

Chowla's conjecture at almost all scales

An unsolved conjecture of Chowla states that the Mobius function should not correlate with its own shifts. This can be viewed as a conjecture about the randomness of the Mobius function.

In the last few years, there has been a lot of progress on Chowla's conjecture. Nearly all of the previously obtained results have concerned correlations that are weighted logarithmically, so one wonders whether it is possible to get rid of these weights. We show that one can indeed remove logarithmic weights from previously known results on Chowla's conjecture, provided that one restricts to almost all scales in a suitable sense.

This is joint work with Terry Tao.