A function \(f\) which satisfies \(f(n)f(m) = f(nm)\) when \(n\) and \(m\) are coprime is called a multiplicative function. Utilizing this behavior, we will be exploring sums of the form \(\sum_{n < x} f(kn)f(ln)\), with fixed \(l\) and \(k\), which we call a multiplicative correlation between \(f(kn)\) and \(f(ln)\). To compute these correlations, we will derive formulas for the Dirichlet generating series whose coefficients are \(a_n = f(kn)f(ln)\), and then use Perron’s Formula. In particular, we will be looking at multiplicative correlations of the Möbius function and the divisor function, which yields insight into the behavior of the square free numbers.

The talk might also be streamed in zoom meeting ID: 986 2892 7517