Infinitely Many Real Quadratic Fields of Class Number One

Abstract

We point out that the results of Adleman and Huang ("Primality Testing and Abelian Varieties over Finite Fields," Lecture Notes in Math., Vol. 1512, Springer-Verlag, Berlin, 1992) imply that there are infinitely many real quadratic function fields over finite fields of ideal class number one. This is in marked contrast to the case of imaginary quadratic function fields over finite fields, of which there are four(J. Algebra17 (1971), 243-261).