Analytic Methods in Arithmetic Geometry (Contemporary (2020)

Analytic Methods in Arithmetic GeometryAuthor(s): Alina Bucur, David Zureick-Brown\nFormat: Paperback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9781470437848, 978-1470437848\nSynopsis\nThis volume contains the proceedings of the Arizona Winter School 2016, which was held from March 12-16, 2016, at The University of Arizona, Tucson, AZ. In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with $mathrm{SL}_2(mathbb{F}_q).