On the class number formula of certain real quadratic fields - Archive ouverte HAL Access content directly
Journal Articles Hardy-Ramanujan Journal Year : 2013

On the class number formula of certain real quadratic fields

Abstract

In this note we give an alternate expression of class number formula for real quadratic fields with discriminant $d \equiv 5\, {\rm mod}\, 8$. %Dirichlet's classical class number formula for real quadratic fields expresses `class number' in somewhat `transcend' manner, which was simplified by P. Chowla in the special case when the discriminant $d = p \equiv 5\,{\rm mod}\, 8$ is a prime. We use another form of class number formula and transform it using Dirichlet's $1/4$-th character sums. Our result elucidates other generalizations of the class number formula by Mitsuhiro, Nakahara and Uhera for general real quadratic fields.
Fichier principal
Vignette du fichier
36Article1.pdf (269.6 Ko) Télécharger le fichier
Origin : Explicit agreement for this submission
Loading...

Dates and versions

hal-01112681 , version 1 (03-02-2015)

Identifiers

Cite

K Chakraborty, S Kanemitsu, T Kuzumaki. On the class number formula of certain real quadratic fields. Hardy-Ramanujan Journal, 2013, Volume 36 - 2013, pp.1 - 7. ⟨10.46298/hrj.2013.178⟩. ⟨hal-01112681⟩

Collections

INSMI
64 View
852 Download

Altmetric

Share

Gmail Facebook X LinkedIn More