Periods of Mixed Tate Motives over Real Quadratic Number Rings

Recently, the author defined multiple Dedekind zeta values \cite{MDZF} associated to a number \(K\) field and a cone \(C\). In this paper we construct explicitly non-trivial examples of mixed Tate motives over the ring of integers in \(K\), for a real quadratic number field \(K\) and a particular cone C. The period of such a motive is a multiple Dedekind zeta values at \((s_1,s_2)=(1,2)\), associated to the pair \((K;C)\), times a nonzero element of \(K\).