On a Theorem of Ono and Skinner

In a recent paper, Ono and Skinner [1998, Ann. of Math.147, 453–470] show that if a half integral weight eigenform g(z) is good, then g(z) has infinitely many coefficients prime to ℓ, for all but finitely many primes ℓ. Their paper ends with the conjecture that all half-integral weight eigenforms (w...

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Bibliographic Details
Published inJournal of number theory Vol. 86; no. 2; pp. 244 - 252
Main Author McGraw, William J
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.02.2001
Subjects
modular forms
modular forms
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Summary:In a recent paper, Ono and Skinner [1998, Ann. of Math.147, 453–470] show that if a half integral weight eigenform g(z) is good, then g(z) has infinitely many coefficients prime to ℓ, for all but finitely many primes ℓ. Their paper ends with the conjecture that all half-integral weight eigenforms (with the exception of certain theta functions) are, in fact, good. We give a brief and elementary proof of the “good” conjecture.
ISSN:0022-314X
1096-1658
DOI:10.1006/jnth.2000.2557