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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk


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On a conjecture of Atkin

P. Guerzhoy1

1University of Hawaii, Department of Mathematics, 2565 McCarthy Mall, Honolulu, HI 96822-2273. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2010, Issue 639, Pages 121–130, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle.2010.013, January 2010

Publication History

Received:
2007-02-23
Revised:
2008-09-20
Published Online:
2010-01-20

Abstract

Let j be the modular invariant. For the primes p ≦ 23 the q-expansion coefficients of Um(j – 744) are multiplicative as it was a Hecke eigenform modulo a power of p which increases with m. This was conjectured by Atkin on the basis of extensive numerical experiments, and is proved in this paper. The cases p = 5, 7 and 11 are under special consideration in this paper.

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[1]
Amanda Folsom, Zachary A. Kent, and Ken Ono
Advances in Mathematics, 2012, Volume 229, Number 3, Page 1586

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