1. ON THE FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF-INTEGRAL WEIGHT.
- Author
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CHOIE, YOUNG JU and KOHNEN, WINFRIED
- Subjects
- *
COEFFICIENTS (Statistics) , *MODULAR forms , *INTEGRALS , *NUMBER theory , *DISCRIMINANT analysis - Abstract
It is known that if the Fourier coefficients a(n)(n ≥ 1) of an elliptic modular form of even integral weight k ≥ 2 on the Hecke congruence subgroup Γ0(N)(N ∈ N) satisfy the bound a(n) ≪f nc for all n ≥ 1, where c > 0 is any number strictly less than k - 1, then f must be cuspidal. Here we investigate the case of half-integral weight modular forms. The main objective of this note is to show that to deduce that f is a cusp form, it is sufficient to impose a suitable growth condition only on the Fourier coefficients a(|D|) where D is a fundamental discriminant with (-1)kD > 0. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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