Algebraic number theory concern the study of the fields obtained by adjoining an algebraic number to the field of rational numbers. The Stark Conjectures postulate a deep connection between special values of the analytically defined L-series of such a number field and algebraic properties of the field. In particular, these Conjectures predict that certain specific elements of the complex numbers obtained from the L-series are actually algebraic elements, the Stark units. In the case of a relative abelian extension of number fields, the Conjectures further predict that these elements, which would be uniquely defined by the analytic data up to a choice of a root of unity, generate abelian extensions of the number field. The Stark Conjectures are among the central questions in algebraic number theory. This investigation is concerned with examining a number of questions regarding these conjectures, continuing and extending prior work of the investigators. This research falls into the general mathematical field of Number Theory. Number theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.
