On the involutions fixing the class of a lattice

Details On the involutions fixing the class of a lattice On the involutions fixing the class of a lattice

2003-01-26

arxiv.org/abs/math/0301308v1

Mathematics

Number Theory

11 pages LaTeX. To appear in Journal of Number Theory

Scientific paper

With any integral lattice \Lambda in n-dimensional euclidean space we associate an elementary abelian 2-group I(\lambda) whose elements represent parts of the dual lattice that are similar to \Lambda. There are corresponding involutions on modular forms for which the theta series of \Lambda is an eigenform; previous work has focused on this connection. In the present paper I(\Lambda) is considered as a quotient of some finite 2-subgroup of O_n(\R). We establish upper bounds, depending only on n, for the order of I(\Lambda), and we study the occurrence of similarities of specific types.

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