Über Zahlen als Zeichen

Ohne Zusammenfassung     

Quaternionic theta constants

We investigate the six quaternionic theta constants introduced by Freitag and Hermann. More precisely we investigate their restrictions to the Hermitian resp. Siegel half-space of degree 2. It turns out that these theta constants generate the graded ring of symmetric Hermitian modular forms for the principal congruence subgroup of level 1 + i over the Gaussian number field resp. of Siegel modular forms for the principal congruence subgroup of level 2 and even weight. As an application we obtain a simple construction of Igusa’s Siegel modular form of degree 2 and weight 30 with respect to the non-trivial character.     

The functional equation for the twisted spinor L-series of genus 2

We prove the functional equation for the twisted spinor L-series of a cuspidal, holomorphic Siegel eigenform for the full modular group of genus 2. It follows from a more general functional equation, valid for Rankin convolutions of paramodular cuspforms. A non-vanishing result for Fourier-Jacabi coefficients of the eigenforms in question is the central pillar of the deduction of the former from the latter functional equation.