Prof. Bas Edixhoven (Universiteit Leiden): How to count vectors with integral coordinates and given length in Rn.

Thursday, 1 November, 16:00-17:00, Snellius, room 174

Abstract: The question will be addressed how fast one can compute the number of ways in which an integer m can be written as a sum of n squares. At the moment the answer is not known. I will explain why I think that if n is even and m is given with its factorisation into primes, this counting can be done in time polynomial in n.log(m). The proposed method uses a generalisation of the main results of joint work with J-M. Couveignes, R. de Jong and F. Merkl on the complexity of the computation of coefficients of modular forms.