On the Fourier coefficients of Modular forms of Half integral weight
SCIE
SCOPUS
- Title
- On the Fourier coefficients of Modular forms of Half integral weight
- Authors
- Choie, YJ; Kohnen, W
- Date Issued
- 2013-12
- Publisher
- World Sci Pub
- 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 Gamma(0)(N) (N is an element of N) satisfy the bound a(n) << (f) n(c) 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(vertical bar D vertical bar) where D is a fundamental discriminant with (- 1)(k) D > 0.
- Keywords
- Fourier coefficient; Ramanujan bound; cusp form; half-integral weight form
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/15440
- DOI
- 10.1142/S1793042113500632
- ISSN
- 1793-0421
- Article Type
- Article
- Citation
- International Journal of Number Theory, vol. 9, no. 8, page. 1879 - 1883, 2013-12
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