Please use this identifier to cite or link to this item:
|Title:||Jacobi identities, modular lattices, and modular towers||Authors:||Chua, K.S.
|Issue Date:||May-2004||Citation:||Chua, K.S., Solé, P. (2004-05). Jacobi identities, modular lattices, and modular towers. European Journal of Combinatorics 25 (4) : 495-503. ScholarBank@NUS Repository. https://doi.org/10.1016/j.ejc.2003.05.002||Abstract:||We give first a simple proof of a generalized Jacobi identity for n-dimensional odd diagonal lattices which specializes to the classical Jacobi identity for the lattice Z2. For Z+ ℓ Z, it recovers a one-parameter family of Jacobi identities discovered recently by Chan, Chua and Solé, used to deduce two quadratically converging algorithms for computing π corresponding to elliptic functions for the cubic and septic bases. Next, motivated by strongly modular lattices for the ten special levels ℓ, where σ1(ℓ) 24, we derive quadratic iterations in these ten special levels generalizing the cubic and septic cases. This also gives a uniform proof of the equations used by N.D. Elkies for 13 of his explicit modular towers. They correspond exactly to the case where all eta terms occur to the same power in his list. This provides a link between strongly modular lattices and modular towers. © 2003 Elsevier Ltd. All rights reserved.||Source Title:||European Journal of Combinatorics||URI:||http://scholarbank.nus.edu.sg/handle/10635/131450||ISSN:||01956698||DOI:||10.1016/j.ejc.2003.05.002|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Nov 26, 2020
WEB OF SCIENCETM
checked on Nov 18, 2020
checked on Nov 21, 2020
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.