Consider the following expression.
$P* = \prod_{\deg P \leq \zeta} P$
So, $\deg P* = \sum\limits_{\deg P \leq \zeta} \deg P = \sum\limits_{j \leq \zeta } j π(j) $ .
I understand how $\deg P* = \sum\limits_{\deg P\leq \zeta} \deg P $.
But I don't know how $\sum\limits_{\deg P \leq \zeta} \deg P = \sum\limits_{j \leq \zeta } j π(j) $ .
Author has not mentioned what $j$ is but he writes $a= \sum\limits_{j\leq 0} a_j t^j \in F_q[t]$ in previous paragraph.
Can you please help me with that.
For more details please see:http://www.math.tau.ac.il/~rudnick/courses/sieves2015.html See page 6 of Lecture 6 ( Squarefrees over a function field) It is taken from these notes. Lemma 5.1