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VOL. 30 | 2001 On $p$-Adic Zeta Functions and Class Groups of $\mathbb{Z}_{p}$-Extensions of certain Totally Real Fields

Abstract

Let $k$ be a totally real field and $p$ an odd prime number. We assume that $p$ splits completely in $k$ and also that Leopoldt's conjecture is valid for $k$ and $p$. In this note, focusing on Greenberg's conjecture, we will report on our recent results concerning $p$-adic special functions and ideal class groups in the cyclotomic ${\mathbb{Z}}_p$-extension of $k$.

Information

Published: 1 January 2001
First available in Project Euclid: 13 September 2018

zbMATH: 1041.11071
MathSciNet: MR1846468

Digital Object Identifier: 10.2969/aspm/03010401

Subjects:
Primary: 11R23
Secondary: 11R29, 11R42

Rights: Copyright © 2001 Mathematical Society of Japan

PROCEEDINGS ARTICLE
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