Hardy-Ramanujan Journal |
In this note we give an alternate expression of class number formula for real quadratic fields with discriminant d≡5mod8. %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≡5mod8 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.