Dirichlet L-series with real and complex characters and their application to solving double sums

A description of the properties of \L with complex characters is given. By using these, together with the more familiar \L with real characters, it is shown how certain two dimensional lattice sums, which previously could not be put into closed form, may now be expressed in this way.Comment: 21 pages, 1 tabl

Vacuum energy for the supersymmetric twisted D-brane in constant electromagnetic field

We calculate vacuum energy for twisted SUSY D-brane on toroidal background with constant magnetic or constant electric field. Its behaviour for toroidal D-brane (p=2) in constant electric field shows the presence of stable minimum for twisted versions of the theory. That indicates such a background maybe reasonable groundstate.Comment: LaTeX, 10 page

Modelling the dynamical evolution of the Bootes dwarf spheroidal galaxy

We investigate a wide range of possible evolutionary histories for the recently discovered Bootes dwarf spheroidal galaxy, a Milky Way satellite. By means of N-body simulations we follow the evolution of possible progenitor galaxies of Bootes for a variety of orbits in the gravitational potential of the Milky Way. The progenitors considered cover the range from dark-matter-free star clusters to massive, dark-matter dominated outcomes of cosmological simulations. For each type of progenitor and orbit we compare the observable properties of the remnant after 10 Gyr with those of Bootes observed today. Our study suggests that the progenitor of Bootes must have been, and remains now, dark matter dominated. In general our models are unable to reproduce the observed high velocity dispersion in Bootes without dark matter. Our models do not support time-dependent tidal effects as a mechanism able to inflate significantly the internal velocity dispersion. As none of our initially spherical models is able to reproduce the elongation of Bootes, our results suggest that the progenitor of Bootes may have had some intrinsic flattening. Although the focus of the present paper is the Bootes dwarf spheroidal, these models may be of general relevance to understanding the structure, stability and dark matter content of all dwarf spheroidal galaxies.Comment: 10 pages, 7 figures, accepted by MNRA

Integrals of K and E from lattice sums

Abstract. We give closed form evaluations for many families of integrals, whose integrands contain algebraic functions of the complete elliptic integrals K and E. Our methods exploit the rich structures connecting complete elliptic integrals, Jacobi theta functions, lattice sums, and Eisenstein series. Various examples are given, and along the way new (including 10-dimensional) lattice sum evaluations are produced

Investigation of the New Local Group Galaxy VV 124

We present the results of our stellar photometry and spectroscopy for the new Local Group galaxy VV 124 (UGC 4879) obtained with the 6-m BTA telescope. The presence of a few bright supergiants in the galaxy indicates that the current star formation process is weak. The apparent distribution of stars with different ages in VV 124 does not differ from the analogous distributions of stars in irregular galaxies, but the ratio of the numbers of young and old stars indicates that VV 124 belongs to the rare Irr/Sph type of galaxies. The old stars (red giants) form the most extended structure, a thick disk with an exponential decrease in the star number density to the edge. Definitely, the young population unresolvable in images makes a great contribution to the background emission from the central galactic regions. The presence of young stars is also confirmed by the [O III] emission line visible in the spectra that belongs to extensive diffuse galactic regions. The mean radial velocity of several components (two bright supergiants, the unresolvable stellar population, and the diffuse gas) is v_h = -70+/-15 km/s and the velocity with which VV 124 falls into the Local Group is v_LG = -12+/-15 km/s. We confirm the distance to the galaxy D = 1.1+/-0.1 Mpc and the metallicity of red giants ([Fe/H] = -1.37) found by Kopylov et al. (2008).VV 124 is located on the periphery of the Local Group approximately at the same distance from M 31 and our Galaxy and is isolated from other galaxies. The galaxy LeoA nearest to it is 0.5 Mpc away.Comment: 10 pages, 8 figures. Accepted for publication in Astronomy Letters (2010, Vol. 36, No. 5, pp. 309-318