Analytic ranks of elliptic curves over number fields

Let $E$ be an elliptic curves over the rational numbers. Let $F$ be a cyclic extension of prime degree $l$. Then, we show that the average of analytic ranks of $E(F)$ over all cyclic extension of prime degree $l$ is at most $2+r_\mathbb{Q}(E)$, where $r_\mathbb{Q}(E)$ is the analytic rank of $E(\mathbb Q)$. This bound is independent of the degree of the cyclic extension. Also, we also obtain some average rank result over $S_d$-fields

Looking for new gluon physics at the Tevatron

The impact of nonrenormalizable gluon operators upon inclusive jet cross sections is studied. Such operators could arise in an effective strong interaction Lagrangian from gluon substructure and would induce observable cross section deviations from pure QCD at high transverse jet energies. Comparison of the theoretical predictions with recent CDF data yields a lower limit on the gluon compositeness scale $\Lambda$. We find \Lambda > 2.03 \TeV at $95\%$~CL

Risk Aversion or Risk Management?: How Measures of Risk Aversion Affect Firm Entry and Firm Survival

The link between measured risk aversion and the decision to become an entrepreneur is well established, but the link between risk preferences and entrepreneurial success is not. Standard theoretical models of occupational choice under uncertainty imply a positive correlation between an individual’s degree of risk aversion and the expected return from an entrepreneurial venture at the time of entry. Because the expected return is the risk neutral equivalent value, a higher expected return implies a higher survival probability, and so more risk averse entrepreneurs should survive more frequently than their less risk averse counterparts. We test that prediction using successive entry cohorts of young entrepreneurs in the National Longitudinal Survey of Youth 1979 (NLSY79). The empirical results soundly reject the prediction: the most successful entrepreneurs are the least risk averse. This surprising finding calls into question the interpretation of common measures of risk aversion as measures of taste for risk. Instead, measured risk attitudes perform as if they are indicators of entrepreneurial ability– the least risk averse are apparently those who can best assess and manage risks. Indeed, our interpretation is consistent with the work of recent experimental studies that find that the less risk averse have higher cognitive ability.