Abstract
A Gaussian Pisot number is an algebraic integer with modulus greater than one whose other conjugates, over the quadratic field Q(−1), are of modulus less than one. Given a nonreal algebraic number α, with modulus greater than one, we prove that there is a nonzero complex number λ such that the series ∑n∈N(Re(λαn)2+Im(λαn)2) converges (resp. such that the sequence ({Re(λαn)},{Im(λαn)})n∈N has a unique limit point), if and only if α is a Gaussian Pisot number (resp. α is a Gaussian Pisot number satisfying P(1)≥2 or deg(P)=2, where P is the minimal polynomial of α over Q).