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We study a family of functions defined in a very simple way as sums of powersof binary Hermitian forms with coefficients in the ring of integers of anEuclidean imaginary quadratic field $K$ with discriminant $d_K$. Using thesefunctions we construct a nontrivial cocycle belonging to the space of paraboliccocycles on Euclidean Bianchi groups. We also show that the average value ofthese functions is related to the special values of $L(\chi_{d_K},s)$. Usingthe properties of these functions we give new and computationally efficientformulas for computing some special values of $L(\chi_{d_K},s)$.

From Binary Hermitian Forms to parabolic cocycles of Euclidean Bianchi groups