Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.19288 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912852055425024 |
|---|---|
| author | Amiri, Farahnaz |
| author_facet | Amiri, Farahnaz |
| contents | This article is the first in a series devoted to computing the class groups of real quadratic fields. We present a new relation between the class number and the index of unit groups. This relation generalizes Hilbert class field theory for real quadratic fields and establishes a bridge between class field theory, composition laws of binary forms of degree $p^n$, and ideal classes of order $p^n$, where p is prime and n is an arbitrary positive integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19288 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing $p$-Class Group Structure in Real Quadratic Fields: A New Approach Amiri, Farahnaz Number Theory This article is the first in a series devoted to computing the class groups of real quadratic fields. We present a new relation between the class number and the index of unit groups. This relation generalizes Hilbert class field theory for real quadratic fields and establishes a bridge between class field theory, composition laws of binary forms of degree $p^n$, and ideal classes of order $p^n$, where p is prime and n is an arbitrary positive integer. |
| title | Computing $p$-Class Group Structure in Real Quadratic Fields: A New Approach |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.19288 |