PreprintCC BY-SA 4.0arXiv
Shintani Cocycle Decomposition of Topological Polylogarithms for Totally Real Fields
Abstract
We compare two cohomological constructions computing special values of partial zeta functions of totally real number fields at nonpositive integers: the Shintani cocycles arising from polyhedral cone decompositions, and the Eisenstein classes obtained from the topological polylogarithm. In particular we prove that the specialization of the topological polylogarithm at a nonzero torsion point coincides in cohomology with the Shintani class up to an explicit sign and error term, and obtain Siegel and Klingen's classical rationality Theorem.
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BibTeX
@misc{bezerra2026shintani,
title = {{Shintani Cocycle Decomposition of Topological Polylogarithms for Totally Real Fields}},
author = {Julio de Mello Bezerra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32363},
eprint = {2610.32363},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32363},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Shintani Cocycle Decomposition of Topological Polylogarithms for Totally Real Fields
AU - Julio de Mello Bezerra
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32363
UR - https://arxiv.org/abs/2610.32363
AB - We compare two cohomological constructions computing special values of partial zeta functions of totally real number fields at nonpositive integers: the Shintani cocycles arising from polyhedral cone decompositions, and the Eisenstein classes obtained from the topological polylogarithm. In particular we prove that the specialization of the topological polylogarithm at a nonzero torsion point coincides in cohomology with the Shintani class up to an explicit sign and error term, and obtain Siegel and Klingen's classical rationality Theorem.
ER -