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On a conjecture of Atkin
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P. Guerzhoy
Published/Copyright:
January 20, 2010
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.
Received: 2007-02-23
Revised: 2008-09-20
Published Online: 2010-01-20
Published in Print: 2010-February
© Walter de Gruyter Berlin · New York 2010
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Articles in the same Issue
- Deformation quantization of surjective submersions and principal fibre bundles
- Complete moduli spaces of branchvarieties
- DG-algebras and derived A∞-algebras
- Subshifts and perforation
- On a conjecture of Atkin
- Mukai duality for gerbes with connection
- The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(ℤ)
- On a conjecture of Borwein, Bradley and Broadhurst
