Random Chowla conjecture

On the random Chowla conjecture

The Chowla conjecture—the prediction that whether an integer has an odd or even number of prime factors has no bearing on whether its neighbours also do—can be stated in terms of sums of Dirichlet characters. We prove that a Steinhaus random multiplicative function, which models randomly selected Dirichlet characters, converges to the standard complex Gaussian, if summed over values of polynomials of degree two or more.