56,097 research outputs found
Regularized inner products of meromorphic modular forms and higher Green's functions
In this paper we study generalizations of quadratic form Poincar\'e series,
which naturally occur as outputs of theta lifts. Integrating against them
yields evaluations of higher Green's functions. For this we require a new
regularized inner product, which is of independent interest
New limb-darkening coefficients and synthetic photometry for model-atmosphere grids at Galactic, LMC, and SMC abundances
New grids of Atlas9 models have been calculated using revised convection
parameters and updated opacity-distribution functions, for chemical
compositions intended to be representative of solar, [M/H] = +0.3, +0.5, Large
Magellanic Cloud (LMC), and Small Magellanic Cloud (SMC) abundances. The grids
cover T(eff) = 3.5-50kK, from log(g) = 5.0 to the effective Eddington limit.
Limb-darkening coefficients and synthetic photometry are presented in the
UBVRIJHKLM, uvby, ugriz, WFCAM, Hipparcos/Tycho, and Kepler passbands for these
models, and for Castelli's comparable `new-ODF' grids. Flux distributions are
given for the new models. The sensitivity of limb-darkening coefficients to the
adopted physics is illustrated
Spectral simplicity and asymptotic separation of variables
We describe a method for comparing the real analytic eigenbranches of two
families of quadratic forms that degenerate as t tends to zero. One of the
families is assumed to be amenable to `separation of variables' and the other
one not. With certain additional assumptions, we show that if the families are
asymptotic at first order as t tends to 0, then the generic spectral simplicity
of the separable family implies that the eigenbranches of the second family are
also generically one-dimensional. As an application, we prove that for the
generic triangle (simplex) in Euclidean space (constant curvature space form)
each eigenspace of the Laplacian is one-dimensional. We also show that for all
but countably many t, the geodesic triangle in the hyperbolic plane with
interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure
- …