Stark'ın sanıları ve Hilbert'ın onikinci problemi

In this study, we state the principal Stark conjecture by defining Stark regulator which is an analogue of the regulator appearing in the Dirichlet Class Number Formula. The conjecture is independent of a choice of a set of places and a certain isomorphism of Q[G]-modules. We state Stark's refinement of this conjecture (`over Z') for abelian L-functions with simple zeros at s=0. This refinement predicts the existence of Stark units and we explain that the field generated over a totally real field k by the Stark units provides an answer to Hilbert's twelfth problem. We also express John Tate's reformulation for this refinement. Then, we give proofs of the conjecture in some simple cases and Stark's computational verification of the conjecture in a specific case. In the last chapter, we state the Rubin-Stark conjecture which is an extension of this conjecture which includes the case of abelian L-functions with higher order zeros at s=0. We end by giving proofs of the conjecture in some cases and showing its relations between the Stark conjecture.