Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.17458 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- For a real quadratic field $K=\mathbb{Q}(\sqrt{D})$, let $K_{\infty}$ denote the cyclotomic $\mathbb{Z}_{p}$-extension of $K$. Greenberg conjectured that the corresponding Iwasawa module $X_{\infty}$ is finite. Building on the work of Mouhib and Movahhedi, we provide new examples of real quadratic fields for which the conjecture holds, when $X_{\infty}$ is cyclic and the prime is $p=2$. Furthermore, we find a fundamental system of units for certain biquadratic fields of the form $\mathbb{Q}(\sqrt{2}, \sqrt{D})$ and show how to use it to calculate the order of $X_{\infty}$.