Automorphisms of even unimodular lattices and unramified Salem numbers

✍ Scribed by Benedict H. Gross; Curtis T. McMullen

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 215 KB
• Volume: 257
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00552-5

✦ Synopsis

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.