Fourier expansion of holomorphic Siegel modular forms with respect to the minimal parabolic subgroup

1999 ◽  
Vol 231 (3) ◽  
pp. 557-588
Author(s):  
Hiroaki Narita
Keyword(s):  
Parabolic Subgroup ◽  
Modular Forms ◽  
Fourier Expansion ◽  
Siegel Modular Forms ◽  
Minimal Parabolic Subgroup

scholarly journals Dirichlet series in the theory of Siegel modular forms

1984 ◽  
Vol 95 ◽  
pp. 73-84 ◽  
Author(s):  
Yoshiyuki Kitaoka
Keyword(s):  
Dirichlet Series ◽  
Eisenstein Series ◽  
Half Space ◽  
Modular Forms ◽  
Fourier Expansion ◽  
Siegel Modular Forms

We are concerned with Dirichlet series which appear in the Fourier expansion of the non-analytic Eisenstein series on the Siegel upper half space Hm of degree m. In the case of m = 2 Kaufhold [1] evaluated them. Here we treat the general cases by a different method.

scholarly journals Modular descent of Siegel modular forms of half integral weight and an analogy of the Maass relation

1986 ◽  
Vol 102 ◽  
pp. 51-77 ◽  
Author(s):  
Yoshio Tanigawa
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Fourier Expansion ◽  
Fourier Coefficients ◽  
Siegel Modular Forms ◽  
Siegel Modular Form ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Maass Relation

In [8], H. Maass introduced the ‘Spezialschar’ which is now called the Maass space. It is defined by the relation of the Fourier coefficients of modular forms as follows. Let f be a Siegel modular form on Sp(2,Z) of weight k, and let be its Fourier expansion, where . Then f belongs to the Maass space if and only if

scholarly journals Higher pullbacks of modular forms on orthogonal groups

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Brandon Williams
Keyword(s):  
Modular Forms ◽  
Differential Operators ◽  
Jacobi Form ◽  
Siegel Modular Forms ◽  
Orthogonal Groups

Abstract We apply differential operators to modular forms on orthogonal groups O ⁢ ( 2 , ℓ ) {\mathrm{O}(2,\ell)} to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form ϕ are theta lifts of partial development coefficients of ϕ. For certain lattices of signature ( 2 , 2 ) {(2,2)} and ( 2 , 3 ) {(2,3)} , for which there are interpretations as Hilbert–Siegel modular forms, we observe that the higher pullbacks coincide with differential operators introduced by Cohen and Ibukiyama.

AVERAGE SIZE OF GAPS IN THE FOURIER EXPANSION OF MODULAR FORMS

2007 ◽  
Vol 03 (02) ◽  
pp. 207-215 ◽  
Author(s):  
EMRE ALKAN
Keyword(s):  
Elliptic Curve ◽  
Modular Forms ◽  
Fourier Expansion ◽  
Complex Multiplication ◽  
Gap Function ◽  
Quantitative Results ◽  
Average Size

We prove that certain powers of the gap function for the newform associated to an elliptic curve without complex multiplication are "finite" on average. In particular we obtain quantitative results on the number of large values of the gap function.

Sign in / Sign up

Export Citation Format

Share Document