On the correlation of completely multiplicative functions

Himadri Ganguli

Let f(n) be an arithmetic function and x > 0, then we define the correlation function C(f,x) = nxf(n)f(n + 1)f(n + 2). In this talk we present an asymptotic formula for C(f,x) in the case when f(n) is a completely multiplicative function and |f(n)|≤ 1 for all n . Let λy(n) denote the truncated Liouville function which equals +1 or -1 according n has odd or even number of prime divisors p y counted with multiplicity. It follows from the main theorem that C(λy,x) = o(x) whenever y = xo(1) and speaks in favour of the Chowla conjecture that C(λ,x) = o(x) where λ is the classical Liouville function.