Automorphisms of even unimodular lattices and unramified Salem numbers

By B. Gross, Curtis T. McMullen. 2002

64 citations recorded by the source corpus.

Abstract In this paper we study the characteristic polynomials S(x)=det(xI−F|IIp,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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7642dd47e6bfd2a58852fcdaa3bebaaaada35127

Citations in the corpus

• Seventy years of Salem numbers (2014, unknown): “Gross and McMullen [48] have shown that if the minimal polynomial S(x) of a Salem number of degree 22 has |S(−1)| = |S(1)| = 1 (which they call the unramified case), then it is the characteristic polynomial of an automorphism of some (nonprojective) K3 surface X. (If the entropy of F is 0, then this”