CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:20171002-152216783

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20171002-152216783

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/jnth.2000.2633DOIArticle
http://www.sciencedirect.com/science/article/pii/S0022314X00926337?via%3DihubPublisherArticle
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
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:03 Oct 2019 18:49

Repository Staff Only: item control page