Abstract
For a totally real number fieldF, the values of partial ray-class zeta-functions at −k,k∈N, may be calculated using generating functions due to Shintani. These are associated to “cone decompositions” inF⊗R which, however, seem rather non-canonical forF≠Q. Motivated by Iwasawa Theory andp-adicL-functions, we obtain new generating functions by passing to a certainp-adic limit in the case [F: Q]=2,h+(F)=1. We investigate these limiting functions, showing that they possess several pleasing properties not shared by Shintani's.
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