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
Keywords:
${\mathbb{Z}}_p$-extensions
,
$p$-adic zetafunctions
,
ideal class groups
,
Iwasawa invariants
Rights: Copyright © 2001 Mathematical Society of Japan