Pierre Dusart, Autour de la fonction qui compte le nombre de nombres premiers [Around the function which counts the number of primes] [数论专业博士学位论文]

The set of positive integers can be decomposed into two large disjointed classes: the prime numbers and the composite numbers. The present work deals with the ¼(x) function which counts the number of primes not greater than x. For large x, a function equivalent to ¼(x) has been known for a hundred years,since when the prime number theorem was shown. We ¯nd sharpe..