The palindromic index -- A measure of ambiguous cycles of reduced ideals without any ambiguous ideal in real quadratic orders (Q1910681)

This paper deals with the theory of ambiguous classes of ideals in real quadratic fields. The author's goal is to ``give a complete overview of the subject including a general criterion for an arbitrary real quadratic order (not necessarily maximal) to have ambiguous cycles of ideals (not necessarily invertible) without any ambiguous ideals in them.'' The notion of the ``palindromic index'' of a reduced ideal is introduced to facilitate the formulation of this criterion. Several numerical examples are presented in detail to illustrate the concepts discussed.