Jacobi identities, modular lattices, and modular towers
type: Item
instance of: scholarly article
title: Jacobi identities, modular lattices, and modular towers
zbMATH Open document ID: 1075.11032
author: Kok Seng Chua
author: Patrick Solé
published in: European Journal of Combinatorics
publication date: 2004-08-06T00:00:00Z
review text: There are proved generalized Jacobi identities related to odd diagonal lattices. Particular cases of lattices give some known Jacobi identities. In [Trans. Am. Math. Soc. 355, 1005--1520 (2003; Zbl 1021.11036)] the Jacobi identities were used to derive quadratic iteration that generalize the AGM iteration in the classical case. Motivated by strongly modular lattices in ten special levels, the authors deduce similar quadratic iterations. This also gives a uniform proof of the equations used by N. D. Elkies for 13 of his explicit modular towers.
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 11F03
Mathematics Subject Classification ID: 11E45
Mathematics Subject Classification ID: 06C05
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 2082043
zbMATH Keywords: Jacobi identity
zbMATH Keywords: modular lattice
zbMATH Keywords: Hecke operator
zbMATH Keywords: quadratic iteration
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
full work available at URL: j.ejc.2003.05.002
OpenAlex ID: W1997926117
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DOI: 10.1016/J.EJC.2003.05.002
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description: scientific article; zbMATH DE number 2082043