On Clifford's theorem for rank-3 bundles

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In this paper we obtain bounds on h⁰(E) where E is a semistable bundle of rank 3 over a smooth irreducible projective curve X of genus g ≥ 2 defined over an algebraically closed field of characteristic 0. These bounds are expressed in terms of the degrees of stability s₁(E), s₂(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.