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On the involutions fixing the class of a lattice

Quebbemann, H.-G. and Rains, E. M. (2003) On the involutions fixing the class of a lattice. Journal of Number Theory, 101 (1). pp. 185-194. ISSN 0022-314X. doi:10.1016/S0022-314X(03)00022-2.

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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 Λis 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 O_n(ℝ). We establish upper bounds, depending only on n, for the order of I(Λ), and we study the occurrence of similarities of specific types.

Item Type:Article
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URLURL TypeDescription Paper
Additional Information:© 2003 Elsevier Science (USA). Received 23 October 2002, Revised 15 November 2002, Available online 16 April 2003.
Subject Keywords:Lattices; Modular; Iso-dual; Involutions; 2-Groups
Issue or Number:1
Record Number:CaltechAUTHORS:20170925-135839254
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Official Citation:H.-G. Quebbemann, E.M. Rains, On the involutions fixing the class of a lattice, Journal of Number Theory, Volume 101, Issue 1, July 2003, Pages 185-194, ISSN 0022-314X, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81815
Deposited By: Tony Diaz
Deposited On:25 Sep 2017 21:08
Last Modified:15 Nov 2021 19:46

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