On the involutions fixing the class of a lattice |
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Authors: | H-G Quebbemann |
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Institution: | a Fachbereich 6 Mathematik, Universität Oldenburg, 26111 Oldenburg, Germany b Center for Communication Research, Institute for Defense Analyses, Princeton, NJ 08540, USA |
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Abstract: | With any integral lattice Λ in n-dimensional Euclidean space we associate an elementary abelian 2-group I(Λ) whose elements represent parts of the dual lattice that are similar to Λ. There are corresponding involutions on modular forms for which the theta series of Λ is an eigenform; previous work has focused on this connection. In the present paper I(Λ) is considered as a quotient of some finite 2-subgroup of . We establish upper bounds, depending only on n, for the order of I(Λ), and we study the occurrence of similarities of specific types. |
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Keywords: | Lattices Modular Iso-dual Involutions 2-Groups |
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