Degeneration of Polylogarithms and Special Values of $L$-Functions for Totally Real Fields

The degeneration of the polylogarithm on the universal abelian scheme over a Hilbert modular variety at the boundary is described in terms of (critical) special values of the $L$-function of the totally real field defining the variety. This gives a relation between the polylogarithm on abelian schemes and special values of $L$-functions.

2000 Mathematics Subject Classification: 11F41, 11G55, 11R42

Keywords and Phrases: Polylogarithms, Hilbert modular varieties, L-functions of totally real fields

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