Lethbridge Number Theory and Combinatorics Seminar: Nathan Ng

Let h be a natural number and f an arithmetic function. The autocorrelation of f is the sum (over all n less than some x) of the product f(n) f(n+h). Such sums play an important role in analytic number theory. For instance, consider the classical arithmetic functions Lambda(n) (the von Mangoldt function), lambda(n) (Liouville's function), and tau_k(n) (the k-th divisor function).  The autocorrelations of these functions are related to the Twin Prime Conjecture, Chowla's conjecture, and to the moments of the Riemann zeta function, respectively.  In this talk I will present a heuristic probabilistic method for deriving a conjecture for the autocorrelation of a multiplicative function.