Computation of partial zeta values at \(s=0\) over a totally real cubic field
Let \(\zeta(s, A)= \sum_{{\mathfrak A}\in A} N{\mathfrak A}^{-s}\) be the partial zeta-function associated to a ray ideal class \(A\) in a totally real cubic field. The author develops a computationally feasible method for evaluation of the special value \(\zeta (0, A)\). His approach is based on the (by now classical) method of T. Shintani. According to the author, his key idea is to use the lattice points on the boundary of the convex hull of the totally positive elements in the Minkowski space lattice corresponding to \(A\), in order to construct a ``more amenable'' fundamental domain, with respect to the action of the group of units in the ``ray''. The author gives a few numerical examples, in hope ``to compile and publish a more extensive list of tables in the not too distant future''.
scientific article; zbMATH DE number 874195