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
1University of Hawaii, Department of Mathematics, 2565 McCarthy Mall, Honolulu, HI 96822-2273. e-mail: (email)
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
- Published Online:
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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