Elliptic Curves over Function Fields
by Douglas Ulmer
Publisher: arXiv 2011
Number of pages: 72
These are the notes from a course of five lectures at the 2009 Park City Math Institute. The focus is on elliptic curves over function fields over finite fields. In the first three lectures, we explain the main classical results (mainly due to Tate) on the Birch and Swinnerton-Dyer conjecture in this context and its connection to the Tate conjecture about divisors on surfaces.
Home page url
Download or read it online for free here:
by Kenneth A. Ribet, William A. Stein - University of Washington
Contents: The Main objects; Modular representations and algebraic curves; Modular Forms of Level 1; Analytic theory of modular curves; Modular Symbols; Modular Forms of Higher Level; Newforms and Euler Products; Hecke operators as correspondences...
by Jozsef Sandor - American Research Press
Contents: on Smarandache's Podaire theorem, Diophantine equation, the least common multiple of the first positive integers, limits related to prime numbers, a generalized bisector theorem, values of arithmetical functions and factorials, and more.
by Pete L. Clark - University of Georgia
The goal is to find and explore open questions in both geometry of numbers -- e.g. Lattice Point Enumerators, the Ehrhart-Polynomial, Minkowski's Convex Body Theorems, Minkowski-Hlawka Theorem, ... -- and its applications to number theory.
by J. E. Cremona - Cambridge University Press
The author describes the construction of modular elliptic curves giving an algorithm for their computation. Then algorithms for the arithmetic of elliptic curves are presented. Finally, the results of the implementations of the algorithms are given.