Geodesic
Degeneration of polylogarithms and special values of $L$-functions for totally real fields
Documenta mathematica, Tome 13 (2008), pp. 131-159
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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.
DOI : 10.4171/dm/246
Classification : 11F41, 11G55, 11R42
Mots-clés : polylogarithms, Hilbert modular varieties, L-functions of totally real fields 
@article{10_4171_dm_246,
     author = {Guido Kings},
     title = {Degeneration of polylogarithms and special values of $L$-functions for totally real fields},
     journal = {Documenta mathematica},
     pages = {131--159},
     year = {2008},
     volume = {13},
     doi = {10.4171/dm/246},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/246/}
}
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Guido Kings. Degeneration of polylogarithms and special values of $L$-functions for totally real fields. Documenta mathematica, Tome 13 (2008), pp. 131-159. doi: 10.4171/dm/246

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