On the exponent of the ideal class groups of complex quadratic fields.

Abstract:

Let $m(d)$ denote the exponent of the ideal class group of the complex quadratic field $Q(\surd d)$, where $d < 0$ is a fundamental discriminant. It is shown that there are only finitely many $d$ for which $m(d) = 3$. Assuming the extended Riemann Hypothesis, it is shown that $m(d) \to \infty {\text { as }}|d| \to \infty$.