Lectures on the Riemann Zeta Function (Paperback)

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.

General

Imprint:	American Mathematical Society
Country of origin:	United States
Series:	University Lecture Series
Release date:	November 2014
Authors:	H. Iwaniec
Dimensions:	229 x 152 x 7mm (L x W x T)
Format:	Paperback
Pages:	119
ISBN-13:	978-1-4704-1851-9
Categories:	Books > Science & Mathematics > Mathematics > General
LSN:	1-4704-1851-7
Barcode:	9781470418519

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