Witt's Theorem for Symplectic Modular Forms

Abstract

LetLdenote a freeZ-module of rank 2nand Φ an alternating bilinear mapping fromL×Linto the rational integersZ. Writing α · β for Φ(α, β), where α, β ∈L, we haveWe shall assume that Φ is non-singular and unimodular (see Bourbaki [1]).Lis now a (symplectic)lattice.