Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Modular functions arising from some finite groups


Author: Larissa Queen
Journal: Math. Comp. 37 (1981), 547-580
MSC: Primary 20C15; Secondary 10D07, 20D08
MathSciNet review: 628715
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In [2] Conway and Norton have assigned a "Thompson series" of the form

$\displaystyle {q^{ - 1}} + {H_1}q + {H_2}{q^2} + \ldots $

to each element m of the Fischer-Griess "Monster" group M and conjectured that these functions are Hauptmoduls for certain genus-zero modular groups. We have found, for a large number of values of N, all the genus-zero groups between $ {\Gamma _0}(N)$ and $ PSL(2,R)$ that have Hauptmoduls of the above form, and this provides the necessary verification that the series assigned in [2] to particular elements of M really are such Hauptmoduls. (Atkin and Fong [1] have recently verified that $ {H_n}(m)$ really is a character of M for all n.) We compute Thompson series for various finite groups and discuss the differences between these groups and M. We find that the resulting Thompson series are all Hauptmoduls for suitable genus-zero subgroups of $ PSL(2,R)$.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 20C15, 10D07, 20D08

Retrieve articles in all journals with MSC: 20C15, 10D07, 20D08


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0628715-7
PII: S 0025-5718(1981)0628715-7
Article copyright: © Copyright 1981 American Mathematical Society