On the distribution of the of Frobenius elements on elliptic curves over function fields

Let $C$ be a smooth projective curve over $\mathbb{F}_q$ with function field $K$, $E/K$ a nonconstant elliptic curve and $\phi:\mathcal{E}\to C$ its minimal regular model. For each $P\in C$ such that $E$ has good reduction at $P$, i.e., the fiber $\mathcal{E}_P=\phi^{-1}(P)$ is smooth, the eigenvalues of the zeta-function of $\mathcal{E}_P$ over the residue field $\kappa_P$ of $P$ are of the form $q_P^{1/2}e^{i\theta_P},q_{P}e^{-i\theta_P}$, where $q_P=q^{\deg(P)}$ and $0\le\theta_P\le\pi$. The goal of this note is to determine given an integer $B\ge 1$, $\alpha,\beta\in[0,\pi]$ the number of $P\in C$ where the reduction of $E$ is good and such that $\deg(P)\le B$ and $\alpha\le\theta_P\le\beta$.Comment: 8 page

ECONOMIC AND ENVIRONMENTAL IMPACTS OF THE POST-1992 CAP REFORMS ON ALENTEJO ECONOMY OF PORTUGAL

This research develops 'Johansen-type' models of agriculture and constructs Input-Output models for assessing the impact of the post-1992 CAP reforms on incomes, employment and the environment in four Alentejo study areas of Portugal. The effects of agricultural output changes on businesses supplying inputs and processing farm output were also assessed by those empirical models.Common Agricultural Policy, Johansen Model, Input-Output Model, Elasticity, Multiplier and Environmental Indicators, Agricultural and Food Policy, Demand and Price Analysis, Research Methods/ Statistical Methods,

AGRICULTURAL PRODUCTIVITY ANALYSIS OF EUROPEAN UNION AND EASTERN REGIONS

This research work uses stochastic frontier analysis (SFA) and data envelopment analysis (DEA) to examine the sources of agricultural productivity growth over time and of productivity differences among countries and regions in European Union over the period 1980-1998. A comparison of the mean productivity scores obtained by the two approaches show that DEA results are higher than in SFA results, because DEA fits a tighter (more flexible) frontier than the translog frontier. This study is a valuable warning for people to be carefully about the effects of the methodology choice upon their results and to use more than one approach if they suspect that it may have some influence.Data Envelopment Analysis, Stochastic Frontier Analysis, Technical Efficiency Change, Technical Change, Total Factor Productivity Change, European Union., Productivity Analysis, Q12, D24,

Reallocating Agricultural Greenhouse Gas Emission in EU15 Countries

This research work uses an alternative approach for modeling agricultural greenhouse gas emissions as an undesirable output, based on the zero sum gains DEA model (ZSG-DEA BCC model). This approach reallocates agricultural greenhouse gas emissions among EU15 countries. The reallocation analysis of greenhouse gas emissions permits countries that increase their emissions negotiate the emissions reduction with the others. This negotiation process might create a quota trade system for agricultural activity.DEA, Zero Sum Gains, Movement along the Efficient Frontier, Smoothed Frontier, Greenhouse Gas Emissions, Environmental Economics and Policy, Q54, Q56,

AGRICULTURAL PRODUCTIVITY ASSESSMENT IN EUROPEAN COUNTRIES

This research work examines levels and trends in global agricultural productivity in fifteen European Union countries and four Eastern European countries that have already applied for European Union membership. The study makes use of data collected from the Food and Agriculture Organization of the United Nations and covers the period 1980-1998. An approach based on Data Envelopment Analysis is used to provide information on the peers of the (inefficient) i-th country and to derive the Malmquist productivity indices. This approach is chosen due to the non-availability of reliable input price data to measure total factor productivity change, technical efficiency change and technical change. Model results show France, Bel-Lux and Italy are on the frontier technology in the period of study. Although Bulgaria and Hungary do not belong to the European Union, these countries are on the frontier technology, too. These results also show that France posts the most spectacular performance, while the Eastern European region is the major performer region and the Mediterranean region is the weakest performer region over the period of study. These results indicate that technical efficiency is not a source of total factor productivity growth. Another interesting result is that there is not a degree of catch-up due to improved technical efficiency along with growth in technical change in European Union Countries and four Eastern European countries.Productivity Analysis,

Assessment of Environment Impact of CAP Reforms on European Agricultural Production Efficiency

The studies of performance and production efficiency have ignored additional products of most transformation processes classified as undesirable outputs. Without the inclusion of the undesirable outputs, the efficiency measurement is a purely technical measure, and it does not account for the interaction of the system with the environment and the impact of policy decisions on the system. Moreover, there are technological dependencies between the desirable and the undesirable outputs which have to be included in the analytical tools used to measure efficiency. The relationships between the desirable and the undesirable outputs motivate the exploration of new areas of the measurement of efficiency to incorporate policy decisions and address new issues. This research develops a formulation that uses goal programming in conjunction with Data Envelopment analysis – known as GoDEA approach – to deal with the conflict between the desirable and the undesirable outputs. This approach is used to assess the environment impact of the Agenda 2000 and the 2003 Common Agricultural Policy reform on agricultural production in fifteen European countries. Model results show that the 2003 CAP reform strengthens environmental policies and has a better performance than the Agenda 2000 for some European countries. The North and Central European countries have been dealing better with environmental issues than the Mediterranean countries.Data Envelopment Analysis, Performance Measurement, Undesirable Outputs, Technological Dependence, Goal Programming, Common Agricultural Policy, Environmental Economics and Policy, CO2, DO1, Q15, Q58,

Rational points on curves over function fields

We provide in this paper an upper bound for the number of rational points on a curve defined over a one variable function field over a finite field. The bound only depends on the curve and the field, but not on the Jacobian variety of the curve