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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.03285 |
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Table of Contents:
- In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally real field. We then prove that the de Rham realization of this polylogarithm gives the Shintani generating class, a cohomology class generating the values of the Lerch zeta functions of the totally real field at nonpositive integers. Inspired by this result, we give a conjecture concerning the specialization of this polylogarithm class at torsion points, and discuss its relation to the Beilinson conjecture for Hecke characters of totally real fields.