Lectures on the Riemann Zeta Function (University Lecture Series) (University Lecture Series, 62) - Softcover

H. Iwaniec

Softcover

ISBN 10: 1470418517 ISBN 13: 9781470418519

Publisher: American Mathematical Society, 2014

Synopsis

The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. There are also technical lemmas which can be useful in a broader context.

About this title

About the Author

H. Iwaniec , Rutgers University, Piscataway, NJ, USA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2014
• Language: English
• ISBN 10: 1470418517
• ISBN 13: 9781470418519
• Binding: Paperback
• Number of pages: 119