Prof. Bas Edixhoven (Universiteit Leiden): How to count vectors with
integral coordinates and given length in **R**^{n}.

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.