Units in families of totally complex algebraic number fields

Multidimensional continued fraction algorithms associated with GLn(ℤk), where ℤk is the ring of integers of an imaginary quadratic field K, are introduced and applied to find systems of fundamental units in families of totally complex algebraic number fields of degrees four, six, and eight

ON HURWITZ CONSTANTS FOR FUCHSIAN GROUPS

ABSTRACT. Explicit bounds for the Hurwitz constants for general cofinite Fuchsian groups have been found. It is shown that the bounds obtained are exact for the Hecke groups and triangular groups with signature (0: 2Ò pÒ q)