What is meant by supported on prime numbers in this context?

Question

I am reading Sieve - Theory from following lecture notes of Prof. Zeev Rudnick: http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html .

I am studying lecture 11 page 6.

But I think you will be able to understand the question without looking at that page:

Text of the paragraph : Section 2 ( Lower Bounds)

To obtain lower bounds we will need more information about our multiplicative function in particular we will need some information about it's behavior on the prime numbers. Let $\omega$ be a non-negative multiplicative function supported on square frees.

Can you please tell what exactly author means by $\omega$ being supported on square frees?

Thanks!

Answer 1

A function $f: X \to \mathbb{R}$ is supported on $A \subseteq X$ if $f(a) \ne 0$ for all $a \in A$. The support of $f$ is the largest set on which $f$ is supported.