A Note on the Divisibility of Class Numbers of Real Quadratic Fields

Abstract

AbstractSuppose g>2 is an odd integer. For real number X>2, define Sg(X) the number of squarefree integers d⩽X with the class number of the real quadratic field Q (d) being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound Sg(X)⪢X1/g−ε holds for any fixed ε>0, which improves a result of Ram Murty