The class number formula for imaginary quadratic fields

It is shown that the class number for negative discriminant D can be expressed in terms of the base B expansions of reduced fractions x|D|, where B is an integer prime to D. This result is then formulated to obtain information about the distribution of the values of !(x), where ! is the quadratic character associated to D. This leads to simplified formulas for the class number in certain cases.

Joseph Lewittes