In his monumental treatise Disquisitiones Arithmeticae, Gauss conjectured that the class number of an imaginary quadratic field with binary quadratic form discriminant tends to infinity with . A proof was finally given by Heilbronn (1934), and Siegel (1936) showed that for any , there exists a constant such that
as . However, these results were not effective in actually determining the values for a given of a complete list of fundamental discriminants such that , a problem known as Gauss's class number problem.
Goldfeld (1976) showed that if there exists a "Weil curve" whose associated Dirichlet L-series has a zero of at least third order at , then for any , there exists an effectively computable constant such that
Gross and Zaiger (1983) showed that certain curves must satisfy the condition of Goldfeld, and Goldfeld's proof was simplified by Oesterlé (1985).