%0 Journal Article %T Classification of non-symplectic automorphisms of order 3 on $K3$ surfaces %A Shingo Taki %J Mathematics %D 2008 %I arXiv %R 10.1002/mana.200810070 %X In this paper, we study non-symplectic automorphisms of order 3 on algebraic $K3$ surface over $\mathbb{C}$ which act trivially on the N\'{e}ron-Severi lattice. In particular we shall characterize their fixed locus in terms of the invariants of 3-elementary lattices. %U http://arxiv.org/abs/0802.1956v2