An elementary proof for a theorem of Thomas and Vasquez

[摘要] yLet F be a totally real cubic field. Then, the group of totally positive units in F acts on R(3) in a natural way. This paper gives an elementary geometric proof for the construction of a fundamental domain for this action by Thomas and Vasquez in [13]. Furthermore, an explicit class number formula for a totally imaginary quadratic extension of F is described. This formula is completely effective, since a method for determining the Hasse's unit index is given. Some numerical examples of class numbers are included. (C) 1995 Academic Press, Inc.

[发布日期] 1995-12-01