Mathematik und Statistik
  Logo der Universität Konstanz
Schwerpunkt Reelle Geometrie und Algebra > Jun.-Prof. Dr. Arno Fehm

French-German Summer School
Galois Theory and Number Theory
Konstanz, July 18-24 2015

organized by Lior Bary-Soroker (Tel Aviv University), Pierre Dèbes (Université de Lille), Arno Fehm (Universität Konstanz), Zeev Rudnick (Tel Aviv University)

Statistical number theory in function fields

Short summary

In this mini-course we will study classical problems in analytic number theory such as: the twin prime conjecture and its generalization the Hardy-Littlewood prime tuple conjecture, the Goldbach conjecture, statistic of primes in short intervals; via their analogous in the function field setting. While in the number field setting these problems are considered beyond reach (in spite of the recent amazing developments by Zhang, by Maynard, and by Tao), in the function field setting some analogues may be completely solved. The function field results shed new light on the number field problems, and in some cases also are used to solve number field problems. The goal of the mini-course is two folded: Firstly, we will give an overview on the abundance of recent developments in the field of number theory in function fields. Secondly, we will give complete proofs of some of the function field results. These proofs are using, among other things, methods from Galois theory, Field Arithmetic, and specialization theory.

Course material

  • Extended abstract of the course [pdf]

Further information

For further information on this course please contact Lior Bary-Soroker.