Diophantine Approximation On Bianchi Groups Original Research Article

A modification of the Ford geometric approach to the problem of approximation of complex numbers by elements of an imaginary quadratic number field is developed. An upper bound for the Hurwitz constant for the field is obtained in terms of the geometry of the isometric fundamental domain for the corresponding Bianchi group. The Hurwitz constants for the fields of discriminant −20 and −24 are found.