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 LinkedIn

More news

17 July 2025

Veni-grants for eleven UG researchers

The Dutch Research Council (NWO) has awarded a Veni grant of up to €320,000 each to eleven researchers of the University of Groningen and the UMCG: Quentin Changeat, Wen Wu, Femke Cnossen, Stacey Copeland, Bart Danon, Gesa Kübek, Hannah Laurens, Adi...
14 July 2025

ERC Proof of Concept grant for Kottapalli and Covi

Professors Ajay Kottapalli and Erika Covi have received Proof of Concept grants from the European Research Council (ERC).
10 July 2025

Dutch Research Agenda funding for nanomedicine research

Prof Dr Anna Salvati, Dr Christoffer Åberg and Prof Dr Siewert-Jan Marrink have been granted a National Science Agenda (NWA) funding to further develop life-saving drugs based on nanotechnology with the NanoMedNL consortium.

Colloquium Mathematics, Professor P. Stevenhagen

More news

Veni-grants for eleven UG researchers

ERC Proof of Concept grant for Kottapalli and Covi

Dutch Research Agenda funding for nanomedicine research