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.     

Measurements of atmospheric mercury with high time resolution: Recent applications in environmental research and monitoring

In the past five years automated high time-resolution measurements of mercury species in ambient air have promoted remarkable progress in the understanding of the spatial distribution, short-term variability, and fate of this priority pollutant in the lower troposphere. Examples show the wide range of possible applications of these techniques in environmental research and monitoring. Presented applications of measurement methods for total gaseous mercury (TGM) include long-term monitoring of atmospheric mercury at a coastal station, simultaneous measurements during a south-to-north transect measurement campaign covering a distance of approximately 800 km, the operation on board of a research aircraft, and the quantification of mercury emissions from naturally enriched surface soils. First results obtained with a new method for the determination of reactive gaseous mercury (RGM) are presented. Typical background concentrations of TGM are between 1.5 and 2 ng m(-3) in the lower troposphere. Concentrations of RGM have been determined at a rural site in Germany between 2 and 35 pg m(-3). Flux measurements over naturally enriched surface soils in the Western U.S.A. have revealed emission fluxes of up to 200 ng Hg m(-1) h(-1) under dry conditions.