An application of the effective Sato-Tate conjecture

Based on the Lagarias-Odlyzko effectivization of the Chebotarev density theorem, Kumar Murty gave an effective version of the Sato-Tate conjecture for an elliptic curve conditional on analytic continuation and Riemann hypothesis for the symmetric power $L$-functions. We use Murty's analysis to give a similar conditional effectivization of the generalized Sato-Tate conjecture for an arbitrary motive. As an application, we give a conditional upper bound of the form $O((\log N)^2 (\log \log 2N)^2)$ for the smallest prime at which two given rational elliptic curves with conductor at most $N$ have Frobenius traces of opposite sign.Comment: 12 pages; v2: refereed versio

The probability that a complete intersection is smooth

Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case of a single hypersurface, due to Poonen. We use this result to give a probabilistic model for the number of rational points of such a complete intersection. A somewhat surprising corollary is that the number of rational points on a random smooth intersection of two surfaces in projective 3-space is strictly less than the number of points on the projective line.Comment: 14 pages; v3: final journal versio

Self-Employment in Germany: The Trend Has Been Increasing for Some Time

Entrepreneurial self-employment in Germany has undergone a strong upturn in the last 20 years. The number of self-employed people rose by 40 percent between 1991 and 2009. The reasons for this development are the catch-up processes in eastern Germany, structural change towards the service sector, and a strong willingness among the highly skilled, the unmarried and among foreigners to enter self-employment. Furthermore, the percentage of women becoming involved in start-ups increased substantially during the monitoring period. The decision to take up self-employment generally pays off: after three years, 38 percent of all entrepreneurs still being active in the market had a higher income, while only 17 percent had a lower income than in their former paid employment position.Entrepreneurship, self-employment, start-ups

Enhanced Acoustic Emission in Relation to the Acoustic Halo Surrounding Active Region 11429

The use of acoustic holography in the high-frequency $p$-mode spectrum can resolve the source distributions of enhanced acoustic emissions within halo structures surrounding active regions. In doing so, statistical methods can then be applied to ascertain relationships with the magnetic field. This is the focus of this study. The mechanism responsible for the detected enhancement of acoustic sources around solar active regions has not yet been explained. Furthermore the relationship between the magnetic field and enhanced acoustic emission has not yet been comprehensively examined. We have used vector magnetograms from the \Helioseismic and Magnetic Imager (HMI) on-board the Solar Dynamics Observatory (SDO) to image the magnetic-field properties in the halo. We have studied the acoustic morphology of an active region, with a complex halo and "glories," and we have linked some acoustic properties to the magnetic-field configuration. In particular, we find that acoustic sources are significantly enhanced in regions of intermediate field strength with inclinations no different from the distributions found in the quiet Sun. Additionally we have identified a transition region between the active region and the halo, in which the acoustic source power is hindered by inclined fields of intermediate field strength. Finally, we have compared the results of acoustic emission maps, calculated from holography, and the commonly used local acoustic maps, finding that the two types of maps have similar properties with respect to the magnetic field but lack spatial correlation when examining the highest-powered regions.Comment: 19 pages, 8 figures, Accepted by Solar Physic

Transactional Community Lawyering

The racial reckoning during the summer of 2020 presented a renewed call to action for movement lawyers committed to collaborating with mobilized clients to advance racial equity and economic justice. During the last thirty years, community lawyering scholarship has made significant interventions into poverty lawyering and provides the theoretical framework for contemporary movement lawyers. Conceptually, community lawyering theory can be implemented in any practice area; however, prevailing narratives and models for community lawyering are based on group advocacy campaigns and, to a lesser extent, individual representation in dispute resolution. Transactional lawyers—who use private ordering to represent business entities as they form, transact, and manage risks—have been largely ignored in community lawyering scholarship, which focuses on governmental policy reform and rights acquisition. As a result, community lawyering scholarship remains inaccessible to many transactional lawyers, who are beginning to form a critical mass in antipoverty representations. Moreover, transactional lawyering theory does not meaningfully address how transactional lawyers can effectively advance social change. To fill this gap in theory and praxis, community lawyering theory needs to evolve to contemplate and respond to the nuances of transactional lawyering if transactional lawyers are to become movement lawyers advancing racial and economic justice. This Article provides the first textured description of “transactional community lawyering”—the intentional application of community lawyering theory into a distinctly transactional practice. It argues that community lawyering theory must evolve to (1) demand structural, not merely cultural, competency; (2) emphasize strategic alliance building to supplement the boundaries of subject matter expertise; and (3) contemplate the impact of digital technologies in expanding community lawyering beyond its traditional geographic limitations in order to integrate transactional lawyers as community lawyers. By so evolving, community lawyering theory would not only better inform antipoverty transactional lawyering but also prepare the next generation of diverse movement lawyers