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. https://resolver.caltech.edu/CaltechAUTHORS:20171002-152216783
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Abstract
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.
| Item Type: | Article | |||||||||
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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 | |||||||||
| DOI: | 10.1006/jnth.2000.2633 | |||||||||
| Record Number: | CaltechAUTHORS:20171002-152216783 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171002-152216783 | |||||||||
| 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, https://doi.org/10.1006/jnth.2000.2633. (http://www.sciencedirect.com/science/article/pii/S0022314X00926337) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 81971 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 02 Oct 2017 22:52 | |||||||||
| Last Modified: | 15 Nov 2021 19:47 |
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