The relation between the class number and the distribution of primes

Abstract

We shall present here a very simple proof of a connection of the distribution of primes and the class number of a quadratic imaginary algebraic number field. All constants in the following are easily computable. No other method is available to compute the class number with exact constants. The following method, however, is based on a conditional hypothesis. Let d-3 (mod 4) and a prime; k(d) the class number of the field R((-d)ll) where R is the rational numbers; ir(z; d, t) the number of primes not greater than z and congruent to t (mod d).