A certain Dirichlet series attached to Siegel modular forms of degree two.
A Dirichlet series for modular forms of degree n
A generalization of Gauss sums and its applications to Siegel modular forms and L-functions associated with the vector space of quadratic forms.
A Hyperbolic Kac-Moody Algebra and the Theory of Siegel Modular Forms of Genus 2.
A note on automorphic forms.
A note on representation of positive definite binary quadratic forms by positive definite quadratic forms in 6 variables
A Note on the Siegel-Eisenstein series of weight 2 on Sp2 (Z).
Action of Hecke operators on products of Igusa theta constants with rational characteristics
An arithmetic of modular function fields of degree two
Andrianov' s L-functions associated to Siegel wave forms of degree two.
Arithmetic of half integral weight theta-series
Automorphic forms and functions with respect to the Jacobi group.
Bemerkung zu einem Satz von J. Igusa und W. Hammond.
Bessel functionals and Siegel modular forms
Certain L-series of Ranking-Selberg type associated to Siegel modular forms of degree g.
Characteristic Twists of a Dirichlet series for Siegel Cusp Forms.
Class numbers, Jacobi forms and Siegel-Eisenstein series of weight 2 on Sp2.
Cohomology of the boundary of Siegel modular varieties of degree two, with applications
Let 𝓐₂(n) = Γ₂(n)∖𝔖₂ be the quotient of Siegel's space of degree 2 by the principal congruence subgroup of level n in Sp(4,ℤ). This is the moduli space of principally polarized abelian surfaces with a level n structure. Let 𝓐₂(n)* denote the Igusa compactification of this space, and ∂𝓐₂(n)* = 𝓐₂(n)* - 𝓐₂(n) its "boundary". This is a divisor with normal crossings. The main result of this paper is the determination of H(∂𝓐₂(n)*) as a module over the finite group Γ₂(1)/Γ₂(n). As an application...
Congruences between Siegel modular forms on the level of group cohomology
Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...
Congruences for Siegel modular forms
We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree . In particular, we determine when an analog of Atkin’s -operator applied to a Siegel modular form of degree is nonzero modulo a prime . Furthermore, we discuss explicit examples to illustrate our results.