In this paper we obtain bounds on $h^0(E)$ where $E$ is a semistable bundle of rank 3 over a smooth irreducible projective curve $X$ of genus $g \geq 2$ defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability $s_1(E)$, $s_2(E)$. We show also that in some cases the bounds are best possible. These results extend recent work of J. Cilleruelo and I. Sols for bundles of rank 2.
"On Clifford's theorem for rank-3 bundles." Rev. Mat. Iberoamericana 22 (1) 287 - 304, May, 2006.