Jacobi identities, modular lattices, and modular towers
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.
scientific article; zbMATH DE number 2082043
scientific article