Suppose E is an elliptic curve over Q of conductor N with complex multiplication (CM) by Q(i), and fE is the corresponding cuspidal Hecke eigenform in S2new(Γ 0(N)). Then nth Fourier coefficient of fE is nonzero in the short interval (X,X + cX1 4) for all X ≥ 0 and for some c > 0. As a consequence, we produce infinitely many cuspidal CM eigenforms f level N > 1 and weight k > 2 for which if(n) ≤ n1 4 holds, for all n ≥ 0. © 2018 World Scientific Publishing Company.

VG Narasimha Kumar Cheraku

Department of Mathematics

S. Kaushik

Fulltext

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Journal	International Journal of Number Theory
Publisher	World Scientific Publishing Co. Pte Ltd
ISSN	17930421