Open Access
Translator Disclaimer
2005 Extremal modular lattices, McKay Thompson series, quadratic iterations, and new series for $\pi$
Kok Seng Chua
Experiment. Math. 14(3): 343-357 (2005).

Abstract

We give 20 new Ramanujan-type formulae and 20 quadratic approximations to {\small $\pi$}, parameterized by extremal modular lattices of minimal square norm 2 and 4, at the ten special levels corresponding to square-free orders of the Mathieu group {\small $M_{23}$}. An algorithm for uncovering rational relations between two given power series that we used to discover some of the explicit relations is also given. Explicit relations parameterized by modular lattices between McKay Thompson series for the group {\small $\Gamma_0(\ell)^+$} and {\small $\Gamma_0(2\ell)+p_j$}, where {\small $p_j$} range over all odd primes dividing the special level {\small $\ell$}, are uncovered.

Citation

Download Citation

Kok Seng Chua. "Extremal modular lattices, McKay Thompson series, quadratic iterations, and new series for $\pi$." Experiment. Math. 14 (3) 343 - 357, 2005.

Information

Published: 2005
First available in Project Euclid: 3 October 2005

zbMATH: 1084.11016
MathSciNet: MR2172712

Subjects:
Primary: 11F03 , 11H31 , 11Y60

Keywords: $\pi$ , $M_{23}$ , Hauptmodul , McKay Thompson series , Modular lattices , quadratic iterations

Rights: Copyright © 2005 A K Peters, Ltd.

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.14 • No. 3 • 2005
Back to Top