MULTIVARIATE NORMAL DISTRIBUTION FOR INTEGRAL POINTS ON VARIETIES

Given a variety with coefficients in Z, we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that this has a multivariate normal distribution. We generalise this to more general Weil divisors, where we obtain a geometric interpretation of the covariance matrix. For our results we develop a version of the Erdos-Kac theorem that applies to fairly general integer sequences and does not require a positive exponent of level of distribution.