Low-lying zeros of elliptic curve L-functions: Beyond the ratios conjecture

We study the low-lying zeros of L-functions attached to quadratic twists of a given elliptic curve E defined over $\mathbb Q$. We are primarily interested in the family of all twists coprime to the conductor of E and compute a very precise expression for the corresponding 1-level density. In particular, for test functions whose Fourier transforms have sufficiently restricted support, we are able to compute the 1-level density up to an error term that is significantly sharper than the square-root error term predicted by the L-functions Ratios Conjecture.Comment: 33 page

Low-lying zeros of quadratic Dirichlet LL-functions: A transition in the Ratios Conjecture

We study the $1$-level density of low-lying zeros of quadratic Dirichlet $L$-functions by applying the $L$-functions Ratios Conjecture. We observe a transition in the main term as was predicted by the Katz-Sarnak heuristic as well as in the lower order terms when the support of the Fourier transform of the corresponding test function reaches the point $1$. Our results are consistent with those obtained in previous work under GRH and are furthermore analogous to results of Rudnick in the function field case.Comment: 15 page

Low-lying zeros of quadratic Dirichlet LL-functions: Lower order terms for extended support

We study the $1$-level density of low-lying zeros of Dirichlet $L$-functions attached to real primitive characters of conductor at most $X$. Under the Generalized Riemann Hypothesis, we give an asymptotic expansion of this quantity in descending powers of $\log X$, which is valid when the support of the Fourier transform of the corresponding even test function $\phi$ is contained in $(-2,2)$. We uncover a phase transition when the supremum $\sigma$ of the support of $\hat \phi$ reaches $1$, both in the main term and in the lower order terms. A new lower order term appearing at $\sigma=1$ involves the quantity $\hat \phi (1)$, and is analogous to a lower order term which was isolated by Rudnick in the function field case.Comment: 19 page

A Simple Pendulum Determination of the Gravitational Constant

We determined the Newtonian Constant of Gravitation G by interferometrically measuring the change in spacing between two free-hanging pendulum masses caused by the gravitational field from large tungsten source masses. We find a value for G of (6.672 34 +/- 0.000 14) x 10^-11 m^3 kg^-1 s^-2. This value is in good agreement with the 1986 Committee on Data for Science and Technology (CODATA) value of (6.672 59 +/- 0.000 85) x 10^-11 m^3 kg^-1 s^-2 [Rev. Mod. Phys. 59, 1121 (1987)] but differs from some more recent determinations as well as the latest CODATA recommendation of (6.674 28 +/- 0.000 67) x 10^-11 m^3 kg^-1 s^-2 [Rev. Mod. Phys. 80, 633 (2008)].Comment: 10 pages, 2 figure

Stellar Variability: A Broad and Narrow Perspective

A broad near-infrared photometric survey is conducted of 1678 stars in the direction of the $\rho$ Ophiuchi ($\rho$ Oph) star forming region using data from the 2MASS Calibration Database. The survey involves up to 1584 photometric measurements in the \emph{J}, \emph{H} and \emph{K$_{s}$} bands with an $\sim$1 day cadence spanning 2.5 years. Identified are 101 variable stars with $\Delta$\emph{K$_{s}$} band amplitudes from 0.044 to 2.31 mag and $\Delta$(\emph{J}-\emph{K$_{s}$}) color amplitudes ranging from 0.053 to 1.47 mag. Of the 72 $\rho$ Oph star cluster members, 79$\%$ are variable; in addition, 22 variable stars are identified as candidate members. The variability is categorized as periodic, long timescale, or irregular based on the \emph{K$_{s}$} time series morphology. The dominant variability mechanisms are assigned based on the correlation between the stellar color and single band variability. Periodic signals are found in 32 variable stars with periods between 0.49 to 92 days. The most common variability mechanism among these stars is rotational modulation of cool starspots. Periodic eclipse-like variability is identified in 6 stars with periods ranging from 3 to 8 days; in these cases the variability mechanism may be warped circumstellar material driven by a hot proto-Jupiter. Aperiodic, long time scale variability is identified in 31 stars with time series ranging from 64 to 790 days. The variability mechanism is split evenly between either variable extinction or mass accretion. The remaining 40 stars exhibit sporadic, aperiodic variability with no discernible time scale or variability mechanism. Interferometric images of the active giant $\lambda$ Andromedae ($\lambda$ And) were obtained for 27 epochs spanning November. 2007 to September, 2011. The \emph{H} band angular diameter and limb darkening coefficient of $\lambda$ And are 2.777 $\pm$ 0.027 mas and 0.241 $\pm$ 0.014, respectively. Starspot properties are extracted via a parametric model and an image reconstruction program. High fidelity images are obtained from the 2009, 2010, and 2011 data sets. Stellar rotation, consistent with the photometrically determined period, is traced via starspot motion in 2010 and 2011. The orientation of $\lambda$ And is fully characterized with a sky position angle and inclination angle of 23$\degree$ and 78$\degree$, respectively

An asymptotic for the average number of amicable pairs for elliptic curves

Amicable pairs for a fixed elliptic curve defined over $\mathbb{Q}$ were first considered by Silverman and Stange where they conjectured an order of magnitude for the function that counts such amicable pairs. This was later refined by Jones to give a precise asymptotic constant. The author previously proved an upper bound for the average number of amicable pairs over the family of all elliptic curves. In this paper we improve this result to an asymptotic for the average number of amicable pairs for a family of elliptic curves.Comment: 27 pages, with an appendix by Sumit Gir

Export structure and growth : a detailed analysis for Argentina

This paper examines recent changes in the structure of Argentine exports and the implications for future growth. The authors find that the current export structure of Argentina is not conducive to future growth because it is dominated by low-productivity goods that tend to be exported by low-income countries. The productivity content of Argentine exports has increased recently although, as of 2004, these changes have been relatively minor. The authors identify products with characteristics similar to those currently exported by Argentina and which are morelikely to foster growth because they would shift the structure of exports more the efficiency frontier. Those products include chemicals and primary products with some degree of value added, including partly processed meat, fish and grains. If economic growth is to be fostered by developing new export products and by increasing the value added of existing exports, there will be a need for sector-specific analysis to address possible market failures. The analysis should focus on issues such as the provision of public goods needed for production (including infrastructure, but also complex intangibles such as sector-specific legislation), possible impediments to effective coordination, sector-specific and economy wide externalities, or barriers to information. This last source of potential market failure is critical to a successful policy framework for exports and growth.Economic Theory&Research,Transport Economics Policy&Planning,Tax Law,Water and Industry,Agribusiness&Markets