To make progress on one of number theory’s most elementary questions, two mathematicians turned to an unlikely source.

imply that the prime number theorem holds in $[x - y,x],\ y=x^\theta $ , if $1-1/b < \theta < 1$ . In Chapter 3, we introduce the weighted zero-density approach due to Heath-Brown and Iwaniec ...

This book was first published in 1952. It is largely devoted to the object of proving the Vinogradov-Goldbach theorem: that every sufficiently large odd number is the sum of three primes. In the ...

Or is the average distance between them staying the same? The Prime Number Theorem, which Riemann first tried to prove when he was proposing his hypothesis, states that the average distance between ...