ELA, Volume 9, pp. 132-137, August 2002, abstract.

Proof of Atiyah's Conjecture for Two Special
Types of Configurations

Dragomir Z. Djokovic

To an ordered N-tuple (x_1,...,x_N) of distinct points in 
the three-dimensional Euclidean space Atiyah has associated 
an ordered N-tuple of complex homogeneous polynomials 
(p_1,...,p_N) in two variables x,y of degree N-1, each p_i 
determined only up to a scalar factor. He has conjectured 
that these polynomials are linearly independent. In this note 
it is shown that Atiyah's conjecture is true for two special 
configurations of N points. For one of these configurations, 
it is shown that a stronger conjecture of Atiyah and Sutcliffe 
is also valid.