Geodesic
Degeneration of polylogarithms and special values of $L$-functions for totally real fields
Documenta mathematica, Tome 13 (2008), pp. 131-159.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11F41, 11G55, 11R42
Keywords: polylogarithms, Hilbert modular varieties, L-functions of totally real fields 
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     author = {Kings, Guido},
     title = {Degeneration of polylogarithms and special values of $L$-functions for totally real fields},
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     volume = {13},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a16/}
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Kings, Guido. Degeneration of polylogarithms and special values of $L$-functions for totally real fields. Documenta mathematica, Tome 13 (2008), pp. 131-159. http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a16/