Quadratic equations over finite fields and class numbers of real quadratic fields
type: Item
instance of: scholarly article
title: Quadratic equations over finite fields and class numbers of real quadratic fields
zbMATH Open document ID: 0898.11043
DOI: 10.1007/BF01305343
author: Takashi Agoh
author: Toshiaki Shoji
published in: Monatshefte für Mathematik
publication date: 1998-11-02T00:00:00Z
full work available at URL: https://eudml.org/doc/178814
review text: The authors look at finite fields \(\mathbb{F}_p\), where \(p>2\) is prime, and derive explicit formulae for the number of points of certain quadratic hypersurfaces in \(\mathbb{F}^n_p\), where \(n\in\mathbb{N}\). Furthermore, they show that the class number of \(\mathbb{Q}(\sqrt p)\) for \(p\equiv 1\pmod 4\) can be expressed in terms of their formulae. They conclude the paper with a formula for the validity of the Ankeny-Chowla conjecture to hold for \(\mathbb{Q}(\sqrt p)\).
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 05A19
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 14J20
zbMATH DE Number: 1156709
zbMATH Keywords: quadratic forms over finite fields
zbMATH Keywords: Weyl groups
zbMATH Keywords: partitions
zbMATH Keywords: combinatorial identities
zbMATH Keywords: real quadratic fields
zbMATH Keywords: quadratic hypersurfaces
zbMATH Keywords: class number
zbMATH Keywords: Ankeny-Chowla conjecture
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
cites work: A note on unit and class number of real quadratic fields
cites work: The class-number of real quadratic number fields
cites work: A further note on the class number of real quadratic fields
cites work: Q3216750
cites work: Upper bounds for class numbers of real quadratic fields
cites work: Unitary reflection groups and cohomology
cites work: Invariants of Finite Reflection Groups
OpenAlex ID: W1966007727
description: scientific article; zbMATH DE number 1156709