On the Torsion Congruence for Zeta Functions of Totally Real Fields
Abstract
In this note, we study the special values for zeta functions of totally real fields using the Shintani's cone decomposition. We prove certain congruence between the special values for zeta functions under the prime degree field extension. This congruence implies the `torsion congruence' proved by Ritter-Weiss which is crucial in the proof of the noncommutative Iwasawa main conjecture for totally real fields.
Keywords
Cite
@article{arxiv.2310.04385,
title = {On the Torsion Congruence for Zeta Functions of Totally Real Fields},
author = {Yubo Jin},
journal= {arXiv preprint arXiv:2310.04385},
year = {2024}
}
Comments
There is a gap in the paper due to a mistake in Proposition 2.1. The elements chosen by Colmez satisfying the Unit Assumption do not generalize the whole unit groups. We are now trying to resolve this problem by considering the sign fundamental domain as in Charollois-Dasgupta-Greenberg (Integral Eisenstein Cocycles on GLn II: Shintani's method)