The maximal size of $h(D)$

By the class number formula, $h(d)=\frac{\sqrt{D}}{\pi} L(1,\chi_d)$. Thus, the maximal size of the class number of an imaginary quadratic field should be governed by the same considerations as the maximal order of the $\zeta$-function on the 1-line.




Back to the main index for L-functions and Random Matrix Theory.