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Class Groups and Modular Lattices

Rains, E. M. (2001) Class Groups and Modular Lattices. Journal of Number Theory, 88 (2). pp. 211-224. ISSN 0022-314X. doi:10.1006/jnth.2000.2633.

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We show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and strongly modular lattices has a natural extension to the class group of a given discriminant, in terms of a certain set of translations. In particular, a 2-dimensional lattice has “extra” modularities essentially when it has order 4 in the class group. This allows us to determine the conditions on D under which there exists a strongly modular 2-dimensional lattice of discriminant D, as well as how many such lattices there are. The technique also applies to the question of when a lattice can be similar to its even sublattice.

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Additional Information:© 2001 Academic Press. Received 12 December 1998, Available online 26 February 2002. The author thanks J. Lagarias for helpful conversations.
Issue or Number:2
Record Number:CaltechAUTHORS:20171002-152216783
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Official Citation:E.M Rains, Class Groups and Modular Lattices, Journal of Number Theory, Volume 88, Issue 2, June 2001, Pages 211-224, ISSN 0022-314X, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81971
Deposited By: Tony Diaz
Deposited On:02 Oct 2017 22:52
Last Modified:15 Nov 2021 19:47

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