Originally published in 1934 in the Cambridge Tracts, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. The major part of the book is devoted ...

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 ...

Nevertheless, the benefits of basic research in number theory—studying the distribution of prime numbers, developing algorithms for testing whether numbers are prime, and finding factors of ...

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

One of the most significant of these questions is the Riemann hypothesis. At its core, the Riemann hypothesis seeks to find and study the pattern and distribution of prime numbers as they get larger ...

Prime numbers are one of the major objects of interest of the mathematical subfield of number theory. One favourite obsession of number theorists is the distribution of prime numbers among all ...