Milnor $$K_2$$ K 2 and p-adic zeta functions for real quadratic fields

Abstract

G. Stevens ( http://math.bu.edu/people/ghs/research.html ) constructed a modular symbol taking values in circular K-groups, which is intimately related to Eisenstein series. We make precise a relationship between his Milnor K-theoretic modular symbol $$\Phi _{MK}$$ and the period integrals of Eisenstein series. The main goal here is to extract from $$\Phi _{MK}$$ a group 1-cocyle on $${{\mathrm{SL}}}_2(\mathbb {Q})$$ with values in differential form valued distributions and use this to construct a p-adic locally analytic distribution which gives a p-adic partial zeta function of a real quadratic field.