Concomitants of ternary quartics and vector-valued Siegel and Teichmüller modular forms of genus three

Some vector valued Siegel modular forms of genus 2

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

Some vector valued Siegel modular forms of genus 3 Eberhard

Estimating Siegel Modular Forms of Genus 2 Using Jacobi Forms

We give a new elementary proof of Igusa's theorem on the structure of Siegel modular forms of genus 2. The key point of the proof is the estimation of the dimension of Jacobi forms appearing in the FourierJacobi development of Siegel modular forms. This proves not only Igusa's theorem, but also gives the canonical lifting from Jacobi forms to Siegel modular forms of genus 2.

Vector valued hermitian and quaternionic modular forms

Cycles with Local Coefficients for Orthogonal Groups and Vector-valued Siegel Modular Forms

The purpose of this paper is to generalize the relation [KM4] between intersection numbers of cycles in locally symmetric spaces of orthogonal type and Fourier coefficients of Siegel modular forms to the case where the cycles have local coefficients. Now the correspondence will involve vector-valued Siegel modular forms. Let V be a non-degenerate quadratic space of dimension m and signature (p,...