On the involutions fixing the class of a lattice

JOURNAL OF NUMBER THEORY

卷:101

Article

Quebbemann, HG ; Rains, EM

关键词: lattices;    modular;    iso-dual;    involutions;    2-groups;   

DOI  :  10.1016/S0022-314X(03)00022-2

来源: Elsevier

【 摘 要 】

With any integral lattice A 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 A 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. (C) 2003 Elsevier Science (USA). All rights reserved.

【 授权许可】

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