A Note on the Divisibility of Class Numbers of Real Quadratic Fields Original Research Article

Suppose g>2 is an odd integer. For real number X>2, define Sg(X) the number of squarefree integers dless-than-or-equals, slantX with the class number of the real quadratic field image (image) being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound Sg(X)much greater-thanX1/g−var epsilon holds for any fixed var epsilon>0, which improves a result of Ram Murty.