Enrico Bombieri publishes in 1965, in his work on the large sieve ("On the large sieve"), the result that would become known as the Bombieri-Vinogradov theorem, on the distribution of prime numbers in arithmetic progressions. The theorem substantially improves on Dirichlet's theorem, showing that the average error when averaging over the modulus within a certain range is much smaller than what can be proved for an individual case; in many applications, the result can substitute for the generalized Riemann hypothesis, still unproven. Bombieri received the Fields Medal in 1974, partly for this work and for his related contributions to number theory.