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.