Stable averages of central values of Rankin-Selberg L-functions: some new variants

As shown by Michel-Ramakrishan (2007) and later generalized by Feigon-Whitehouse (2008), there are "stable" formulas for the average central L-value of the Rankin-Selberg convolutions of some holomorphic forms of fixed even weight and large level against a fixed imaginary quadratic theta series. We obtain exact finite formulas for twisted first moments of Rankin-Selberg L-values in much greater generality and prove analogous "stable" formulas when one considers either arbitrary modular twists of large prime power level or real dihedral twists of odd type associated to a Hecke character of mixed signature.Comment: 25 pages; typos corrected in corollaries to Thm 1.2, substantial details added to Sec 2.2--2.3, minor changes throughou

Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule

Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction of the transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206(2), -0.32(1), and -0.76(10). At each transition point, we estimate the latent heat as Q=0.356(30), 0.08(3), and 0.05(5), respectively

Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures, dubbed "grain boundary scars", that form around an irreducible density of curvature-induced disclinations in an otherwise hexagonal background. We investigate the structure and the dynamics of these grain boundary scars

On a General Computer Algorithm for the Analysis of Models with Limited Dependent Variables

Several econometric models for the analysis of relationships with limited dependent variables have been proposed, including the probit, Tobit, two-limit probit, ordered discrete, and friction models. Widespread application of these methods has been hampered by the lack of suitable computer programs. This paper provides a concise survey of the various models; suggests a general functional model under which they may be formulated and analyzed; reviews the analytic problems and the similarities and dissimilarities of the models; and outlines the appropriate and necessary methods of analysis including, but not limited to, estimation. It is thus intended to serve as a guide for users of the various models, for the preparation of suitable computer programs, for the users of those programs; and, more specifically, for the users of the program package utilizing the functional model as implemented on the NBER TROLL system.