Kings, Guido Degeneration of polylogarithms and special values of \(L\)-functions for totally real fields. (English) Zbl 1183.11024 Doc. Math. 13, 131-159 (2008). A conjecture of Zagier describes the values of \(L\)-functions of a number fields in terms of polylogs. The present paper uses the functoriality of the topological polylog on the universal abelian scheme over a Hilbert modular variety to describe the degeneration of certain Eisenstein classes in terms of special values of partial \(L\)-functions. The problem is reduced to explicit computations of Nori and Sczech, which are reproduced in the paper. The main result was also proved by Blottière, using different methods Reviewer: Claus M. Sorensen (Princeton) Cited in 2 Documents MSC: 11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11G55 Polylogarithms and relations with \(K\)-theory 11R42 Zeta functions and \(L\)-functions of number fields Keywords:polylogarithms; Hilbert modular varieties; special values of L-functions PDFBibTeX XMLCite \textit{G. Kings}, Doc. Math. 13, 131--159 (2008; Zbl 1183.11024) Full Text: arXiv EuDML EMIS