Fourier coefficients of Siegel cusp forms of degree two

Estimates for Fourier coefficients of Siegel cusp forms

“…also [5] where (10) was deduced by a slightly different reasoning). Nevertheless we feel that the case j = 2 eventually could be handled using similar arguments as in [9]; it would be very interesting to investigate what exponents for ,rag_ 2 (T) and det T would come out. First instead of looking at the expansion (7) one could more generally fix an integer j with 1 < j < O -1 and expand the function F into a Fourier-Jacobi series with the coefficients depending on the variable (z,z)~xC ~j'g~ and being cusp forms on the Jacobi group Fg_j~,<(Z ~J'9-J~ x 7Z.cJ.g-JJ).…”

Estimates for fourier coefficients of siegel cusp forms of degree two, II

“…Let F be a Siegel cusp form of integral weight k on Γ 2 : = Sp 2 (Z) and denote by a(T) (T a positive definite symmetric half-integral (2,2)-matrix) its Fourier coefficients. In [2] Kitaoka proved that (1) a(T) « ε , F (det T) k/2~1/4+ε (ε > 0) (the result is actually stated only under the assumption that k is even).…”

On Fourier coefficients of Siegel modular forms.

“…For r = l, 2 we may take (for any ε>0) by the Ramanujan-Petersson-conjecture proved by Deligne and a result of Kitaoka's [14] respectively. For r = l, 2 we may take (for any ε>0) by the Ramanujan-Petersson-conjecture proved by Deligne and a result of Kitaoka's [14] respectively.…”

“…This method was generalized to Siegel cusp forms of degree 2 by Kitaoka [14]. The approach of Kitaoka can be modified to work also for Maa -Poincare series [21] attached to the matrices l J e A 2 with t ^ 1.…”