= Solution
Given $f$, choose the <hyperplane divisors> as in (a). The ratios $f_Q$ form a <linear subspace> of $L(D)$ by (d), and its <dimension> equals $md+1-g=\ell(D)$ by (b). A <linear subspace> of a finite-dimensional <vector space> with the same <dimension> is the whole space. Hence $f=f_Q$ for some homogeneous <polynomial> $Q$ of degree $m$, giving
$$
\boxed{f([x:y:z])=\frac{Q(x,y,z)}{\prod_{i=1}^m(a_ix+b_iy+c_iz)}.}
$$
The zero function corresponds to $Q=0$. Thus every allowed <meromorphic function> is a ratio of homogeneous <polynomials> of equal degree, with a denominator that can be chosen as a product of linear forms.
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