关于全实域 zeta 函数的挠同余
数论
2024-02-02 v2
摘要
在本注记中,我们利用 Shintani 锥分解研究全实域 zeta 函数的特殊值。我们证明了在素数次域扩张下 zeta 函数特殊值之间的某种同余。该同余蕴含了 Ritter-Weiss 所证明的、在全实域非交换 Iwasawa 主猜想证明中至关重要的“挠同余”。
引用
@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}
}
备注
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)