Identities for Anderson generating functions for Drinfeld modules

Anderson generating functions are generating series for division values of points on Drinfeld modules, and they serve as important tools for capturing periods, quasi-periods, and logarithms. They have been fundamental in recent work on special values of positive characteristic L-series and in transcendence and algebraic independence problems. In the present paper we investigate techniques for expressing Anderson generating functions in terms of the defining polynomial of the Drinfeld module and determine new formulas for periods and quasi-periods.Comment: 18 page

Exploring Refugee Administration Systems in Egypt, Jordan, and Uganda: A Comparative Study

In this study, I compare three refugee administration models in the global south to one another: Egypt’s, Jordan’s, and Uganda’s. This research is conducted at what I believe is a curious moment of history, where host countries in the global south are encouraged by wealthier states to accept aid in exchange for keeping migrants in the south. In these circumstances, refugee administration models in host countries continue to operate, and new political approaches arise, such as the “Jordan Refugee Compact”. The aim of the comparative study is to spot both the successes and failures of each model in the three countries in terms of meeting the states’ obligations as per international law. I also assess new approaches adopted by some states, spot the lessons learned, and conclude by formulating my recommendations for improving further the existing model in Egypt

On the Atkin Polynomials

We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials. This shows that co-recursive polynomials may lead to interesting sets of orthogonal polynomials.Comment: 18 pages. Accepted for publication at the Pacific Journal of Mathematic