Colloquium Mathematics, Prof. Bas Edixhoven

Join us for coffee and tea at 15.45 p.m.

Date: Tuesday, January 24^th 2012

Speaker: Prof. Bas Edixhoven
               University Leiden

Room: 5161.0267 (Bernoulliborg),

Time:  16.15

Title:Fast computation of the number of vectors of given length in a lattice.

Abstract:

The question is how one can compute the number of ways in which an integer m can be written as a sum of n squares of integers, fast. I will explain how recent progress in computation of 2-dimensional Galois representations make it possible to compute this number, for n even and m given with its factorisation in prime numbers, in time at most a power of n.log(m) (assuming the Riemann hypothesis for number fields). This is an application of a generalisation by Peter Bruin of joint work of the speaker with Jean-Marc Couveignes, Robin de Jong and Franz Merkl.

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)