ON THE FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF-INTEGRAL WEIGHT
2013 ◽
Vol 09
(08)
◽
pp. 1879-1883
◽
Keyword(s):
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.
2010 ◽
Vol 06
(01)
◽
pp. 69-87
◽
2013 ◽
Vol 16
◽
pp. 216-245
2012 ◽
Vol 08
(03)
◽
pp. 749-762
◽
Keyword(s):
2013 ◽
Vol 149
(12)
◽
pp. 1963-2010
◽
2018 ◽
Vol 88
(2)
◽
pp. 371-376
Keyword(s):
Keyword(s):