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In this paper we present a classification of non-symplectic automorphisms ofK3 surfaces whose order is a multiple of seven by describing the topologicaltype of their fixed locus. In the case of purely non-symplectic automorphisms,we provide new results for order 14 and alternative proofs for orders 21, 28and 42, so that we can unify in the same paper the results on theseautomorphisms. For each of these orders we also consider not purelynon-symplectic automorphisms and obtain a complete characterization of theirfixed loci. Several results of our paper were obtained independently in arecent paper by Brandhorst and Hofmann, but the methods used in the two papersare completely different.

Non-symplectic automorphisms of order multiple of seven on K3 surfaces