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 nontrivial 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 HardyLittlewood. 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 onethird of nontrivial 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 Henryk Iwaniec
H. Iwaniec , Rutgers University, Piscataway, NJ, USA.Details Book
Author  :  Henryk Iwaniec 
Publisher  :  American Mathematical Society 
Data Published  :  30 November 2014 
ISBN  :  1470418517 
EAN  :  9781470418519 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  119 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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