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arXiv · 2601.19288

Computing $p$-Class Group Structure in Real Quadratic Fields: A New Approach

Farahnaz Amiri
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Abstract

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.

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Farahnaz Amiri. 2026-01-27. Computing $p$-Class Group Structure in Real Quadratic Fields: A New Approach. https://arxiv.org/abs/2601.19288

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