Skip to ContentSkip to Navigation
University of Groningenfounded in 1614  -  top 100 university
Close
About us Latest news News News articles

Colloquium Mathematics, Professor P. Stevenhagen

24 June 2014

Join us for coffee and tea at 15.30 p.m.

Date:                      

Tuesday, June 24th 2014

Speaker:

Prof. Peter Stevenhagen,
University Leiden

Room:

5161.0293 (Bernoulliborg)

Time:

16.00

Title:   From Artin’s conjecture to Serre curves


Abstract:

In 1927, the German mathematician Emil Artin conjectured that for any non-square integer x different from -1, the powers of x will fill up all (non-zero) residue classes modulo a prime number p for infinitely many p. For instance, the powers of 2 fill up the residue classes modulo 3, 5, and 11, but not modulo 7 or 17. The conjecture also predicts a density for the set of such primes p, which for x=2 it is about 37%. I will explain why the conjecture is still unproved for all values of x, but can be proved if one is willing to assume the generalized Riemann hypothesis. Then, I will focus on the computation of the associated densities, for which Artin made a mistake that was only discovered after computer calculations in the 1950’s(!). The computation of such densities now be realized in a more conceptual way that allows various generalizations, of which I will discuss the example of Serre curves. These are elliptic curves over the rationals for which the associated Galois representation on their torsion points is `maximal’ in a sense that I will define.

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and
 Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl )

http://www.rug.nl/research/jbi/news/colloquia/mathematics-colloquia/

Last modified:10 February 2021 2.27 p.m.
Share this Facebook Twitter LinkedIn

More news

Follow the UGfacebook twitter linkedin rss instagram youtube
Functional
Provides basic functions and uses anonymized cookies.
Standard
Provides optimal operation and uses video cookies, among others.
Complete
Provides personalized content and uses marketing cookies.
Set your cookie preferences. Read our privacy and cookie disclaimer for more information.