# Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers

 Title: Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers Author: Gross, Benedict H.; McMullen, Curtis T. Note: Order does not necessarily reflect citation order of authors. Citation: Gross, Benedict H., and Curtis T. McMullen. 2002. Automorphisms of even unimodular lattices and unramified Salem numbers. Journal of Algebra 257(2): 265-290. Revised 2008. Full Text & Related Files: McMullen_AutomorphismUnimodular.pdf (326.1Kb; PDF) Abstract: In this paper we study the characteristic polynomials $$S(x)=\det(xI−F| II_{p,q})$$ of automorphisms of even unimodular lattices with signature $$(p,q)$$. In particular, we show that any Salem polynomial of degree $$2n$$ satisfying $$S(−1)S(1)=(−1)^n$$ arises from an automorphism of an indefinite lattice, a result with applications to K3 surfaces. Published Version: doi:10.1016/S0021-8693(02)00552-5 Other Sources: http://www.math.harvard.edu/~ctm/papers/index.html Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3446009 Downloads of this work: