Rudnick and Soundararajan's Theorem for Function Fields

In this paper we prove a function field version of a theorem by Rudnick and Soundararajan about lower bounds for moments of quadratic Dirichlet $L$-functions. We establish lower bounds for the moments of quadratic Dirichlet $L$--functions associated to hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_{q}$ in the large genus $g$ limit.Comment: 18 pages, to appear in Finite Fields and Their Application

All the solutions of the form M2(warped)x\Sigma(d-2) for Lovelock gravity in vacuum in the Chern-Simons case

In this note we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension greater than four. The spacetime is characterized by admitting a metric that is a warped product of a two-dimensional spacetime M2 and an (a priori) arbitrary Euclidean base manifold Sigma(d-2) of dimension d-2. We show that the solutions are naturally classified in terms of the equations that restrict the base manifold. According to the strength of such constraints we found the following branches in which Sigma(d-2) has to fulfill: a Lovelock equation with a single vacuum (Euclidean Lovelock Chern-Simons in dimension d-2), a single scalar equation that is the trace of an Euclidean Lovelock CS equation in dimension d-2, or finally a degenerate case in which the base manifold is not restricted at all. We show that all the cases have some degeneracy in the sense that the metric functions are not completely fixed by the field equations. This result extends the static five-dimensional case previously discussed in Phys.Rev. D76 (2007) 064038, and it shows that in the CS case, the inclusion of higher powers in the curvature does not introduce new branches of solutions in Lovelock gravity. Finally we comment on how the inclusion of a non-vanishing torsion and matter fields may modify this analysis.Comment: 15 pages, no figure

Thermodynamic properties of the XX model in a chain with a period two and three coupling

The exact solutions for the energy spectrum of the XX model with a periodic coupling and an external transverse magnetic field $h$ are obtained. The diagonalization procedure is discussed, and analytical and numerical solutions are given. Using the solutions for period-two coupling, the free energy, entropy, and specific heat are calculated as functions of temperature and applied transverse external magnetic field. Their expressions show that below a particular value $v$ and above a value $u$ of the magnetic field $|h|$, the entropy and the specific heat vanish exponentially in the low temperature limit.Comment: 20 pages, 9 figures, new references adde

The Conversion Rate of R&D into Technological Innovation in Family-Managed Firms Under Vulnerability

This paper primarily questions whether under vulnerability, decision-makers will be able to turn R&D into technological innovation more efficiently in order to increase the likelihood of firm survival (Palmer & Wiseman, 1999), using divergences between current firm performance and both historical and social performance as indicators of aspirations gaps (Lant, 1992; Wiseman & Gómez-Mejia, 1998). Then, we look whether the level family management and the level of slack may moderate the effect of performance below aspiration levels on the relationship between R&D intensity and the likelihood of obtaining technological innovation.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec