Abstract
We discuss a variant of the density and energy increment arguments that we call an "entropy decrement method", which can be used to locate a scale in which two relevant random variables share very little mutual information, and thus behave somewhat like independent random variables. We were able to use this method to obtain a new correlation estimate for multiplicative functions, which in turn was used to establish the Erdos discrepancy conjecture that any sequence taking values in {-1,+1} had unbounded sums on homogeneous arithmetic progressions.