Prime numbers between squares
Received: 13 January 2004
Revised: 11 May 2004
Mathematics Subject Classification (2000): 11N05
Abstract: A well known conjecture about the distribution of primes asserts that between two consecutive squares there is always at least one prime number. The proof of this conjecture is out of reach at present, even under the assumption of the Riemann Hypothesis. The aim of this paper is to provide a conditional proof of the conjecture assuming a hypothesis about the behavior of Selberg's integral in short intervals.