p-Adic Limits of Shintani Generating Functions for a Real Quadratic Field Original Research Article

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