Lectures on the Riemann Zeta Function is popular PDF and ePub book, written by H. Iwaniec in 2014-10-07, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lectures on the Riemann Zeta Function can be Read Online from any device for your convenience.
Lectures on the Riemann Zeta Function Book PDF Summary
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.
Detail Book of Lectures on the Riemann Zeta Function PDF
- Author : H. Iwaniec
- Release : 07 October 2014
- Publisher : American Mathematical Society
- ISBN : 9781470418519
- Genre : Mathematics
- Total Page : 130 pages
- Language : English
- PDF File Size : 8,7 Mb
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