On Class Numbers of Real Quadratic Fields with Certain Fundamental Discriminants

Abstract

Let $N$ denote the sets of positive integers and $D \inN$ be square free,and let $\chi_D$ ,  $h = h(D)$ denote the non-trivial Dirichlet character, the class number of the real quadratic eld $K = Q\sqrt(D)$, respectively ONO, proved the theorem in [8] by applying Sturm's Theorem on the congruence of modular form to Cohen's half integral weight modular forms. Later, Dongho Byeon proved a theorem and corollary in [1] by rening Ono' methods. In this paper, we will give a theorem for certain real quadratic fields. by considering  above mentioned studies. To do this, we shall obtain an upper bound different from current bounds for $L(1; \chi_D)$ and use Dirichlet's class number formula.