Kings, Guido

Degeneration of polylogarithms and special values of $L$-functions for totally real fields

Doc. Math., J. DMV 13, 131-159 (2008)

Summary

Summary: 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.

Mathematics Subject Classification

11F41, 11G55, 11R42

Keywords/Phrases

polylogarithms, Hilbert modular varieties, L-functions of totally real fields

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