10.46298/hrj.2013.178
Chakraborty, K
K
Chakraborty
Kanemitsu, S
S
Kanemitsu
Kuzumaki, T
T
Kuzumaki
On the class number formula of certain real quadratic fields
episciences.org
2013
Real quadratic field
class number formula
[MATH] Mathematics [math]
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Journal article
https://hrj.episciences.org/178
https://hal.archives-ouvertes.fr/hal-01112681v1
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Hardy-Ramanujan Journal ; Volume 36 - 2013
International audience
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.