Back to Search
Start Over
ON THE FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF-INTEGRAL WEIGHT.
- Source :
-
International Journal of Number Theory . Dec2013, Vol. 9 Issue 8, p1879-1883. 5p. - Publication Year :
- 2013
-
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]
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 9
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 92672622
- Full Text :
- https://doi.org/10.1142/S1793042113500632