And then there were infinitely many -- Asymptotic estimates -- Combinatorial ways to count primes -- The Dirichlet convolution -- Dirichlet series -- An explicit formula for counting primes -- The Riemann zeta function -- The Perron inversion formula -- The prime number theorem …
And then there were infinitely many -- Asymptotic estimates -- Combinatorial ways to count primes -- The Dirichlet convolution -- Dirichlet series -- An explicit formula for counting primes -- The Riemann zeta function -- The Perron inversion formula -- The prime number theorem …
Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical re…
"Searching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap lengt…
"This book presents the development of Prime Number Theory from its beginnings until the end of the first decade of the xxth century. Special emphasis is given to the work of Cebysev, Dirichlet, Riemann, Vallee-Poussin, Hadamard and Landau. The book presents the principal result…
