### About this book

- Contains recent advances and results in number theory
- Collects papers never before published in book form
- Explains the Riemann Hypothesis to someone without a background in complex analysis

The Riemann Hypothesis has become the Holy Grail of mathematics in the
century and a half since 1859 when Bernhard Riemann, one of the
extraordinary mathematical talents of the 19th century, originally
posed the problem. While the problem is notoriously difficult, and
complicated even to state carefully, it can be loosely formulated as
"the number of integers with an even number of prime factors is the
same as the number of integers with an odd number of prime factors."

The Hypothesis makes a very precise connection between two seemingly
unrelated mathematical objects, namely prime numbers and the zeros of
analytic functions. If solved, it would give us profound insight into
number theory and, in particular, the nature of prime numbers.

This book is an introduction to the theory surrounding the Riemann
Hypothesis. Part I serves as a compendium of known results and as a
primer for the material presented in the 20 original papers contained
in Part II. The original papers place the material into historical
context and illustrate the motivations for research on and around the
Riemann Hypothesis. Several of these papers focus on computation of
the zeta function, while others give proofs of the Prime Number
Theorem, since the Prime Number Theorem is so closely connected to the
Riemann Hypothesis.

The text is suitable for a graduate course or seminar or simply as a
reference for anyone interested in this extraordinary conjecture.

Written for:

Professional/practitioner