K Chakraborty ; S Kanemitsu ; T Kuzumaki - On the class number formula of certain real quadratic fields

hrj:178 - Hardy-Ramanujan Journal, January 1, 2013, Volume 36 - 2013 - https://doi.org/10.46298/hrj.2013.178
On the class number formula of certain real quadratic fieldsArticle

Authors: K Chakraborty 1; S Kanemitsu 2; T Kuzumaki 3

In this note we give an alternate expression of class number formula for real quadratic fields with discriminant d5mod8. %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=p5mod8 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.


Volume: Volume 36 - 2013
Published on: January 1, 2013
Imported on: March 3, 2015
Keywords: Real quadratic field,class number formula,[MATH]Mathematics [math]

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