Article Dans Une Revue Hardy-Ramanujan Journal Année : 2013

On the class number formula of certain real quadratic fields

Résumé

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.
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Dates et versions

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

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Citer

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⟩
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