Zeroes of transfer function
Consider a simpler one-rung ladder with just L2/C4 and C3/L1/R3.
Let the impedance of L2/C4 be:
$$\small Z_1=\frac{a+bs}{c+ds}$$ and the impedance of C3/L1/R3: $$\small Z_2=\frac{e+fs}{g+hs}$$ where \$\small s\$ is the Laplace operator.
The transfer function is $$\small G(s)=\frac{Z_2}{Z_1+Z_2} =\frac{(e+fs)(c+ds)}{(g+hs)(a+bs)+(e+fs)(c+ds)}$$
There will be transfer function zeros when the numerator is zero, i.e. when: $$\small (e+fs)=0 \:\: or \:\:(c+ds) =0$$
i.e., at the zero of \$\small Z_2\$, or the pole of \$\small Z_1\$.