Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

uvbyHbeta photometry of main sequence A type stars.

We present Stroemgren uvby and Hbeta_ photometry for a set of 575 northern main sequence A type stars, most of them belonging to the Hipparcos Input Catalogue, with V from 5mag to 10mag and with known radial velocities. These observations enlarge the catalogue we began to compile some years ago to more than 1500 stars. Our catalogue includes kinematic and astrophysical data for each star. Our future goal is to perform an accurate analysis of the kinematical behaviour of these stars in the solar neighbourhood.

Detection of moving groups among early type stars

Our procedure to detect moving groups in the solar neighbourhood (Chen et al., 1997) in the four-dimensional space of the stellar velocity components and age has been improved. The method, which takes advantadge of non-parametric estimators of density distribution to avoid any a priori knowledge of the kinematic properties of these stellar groups, now includes the effect of observational errors on the process to select moving group stars, uses a better estimation of the density distribution of the total sample and field stars, and classifies moving group stars using all the available information. It is applied here to an accurately selected sample of early-type stars with known radial velocities and Strömgren photometry. Astrometric data are taken from the HIPPARCOS catalogue (ESA, 1997), which results in an important decrease in the observational errors with respect to ground-based data, and ensures the uniformity of the observed data. Both the improvement of our method and the use of precise astrometric data have allowed us not only to confirm the existence of classical moving groups, but also to detect finer structures that in several cases can be related to kinematic properties of nearby open clusters or associations.

A type stars - physical parameters from UVBY and H-beta photometry

uvby H-beta photometry has been obtained for a sample of 93 selected main sequence A stars. The purpose was to determine accurate effective temperatures, surface gravities, and absolute magnitudes for an individual determination of ages and parallaxes, which have to be included in a more extensive work analyzing the kinematic properties of A V stars. Several calibrations and methods to determine the above mentioned parameters have been reviewed, allowing the design of a new algorithm for their determination. The results obtained using this procedure were tested in a previous paper using uvby H-beta data from the Hauck and Mermilliod catalogue, and comparing the rusulting temperatures, surface gravities and absolute magnitudes with empirical determinations of these parameters.