Author: H. Iwaniec
Publisher: American Mathematical Society
ISBN: 1470418517
Category : Mathematics
Languages : en
Pages : 130
Book Description
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.
Lectures on the Riemann Zeta Function
Author: H. Iwaniec
Publisher: American Mathematical Society
ISBN: 1470418517
Category : Mathematics
Languages : en
Pages : 130
Book Description
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.
Publisher: American Mathematical Society
ISBN: 1470418517
Category : Mathematics
Languages : en
Pages : 130
Book Description
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.
Lectures on the Riemann Zeta-function
Author: Komaravolu Chandrasekharan (mathematician)
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 304
Book Description
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 304
Book Description
Lectures on Mean Values of the Riemann Zeta Function
Author: A. Ivić
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 388
Book Description
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 388
Book Description
Lectures on the Riemann Zeta-function
Author: Komaravolu Chandrasekharan
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 390
Book Description
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 390
Book Description
Lectures on the Mean-value and Omega-theorems for the Riemann Zeta-function
Author: K. Ramachandra
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 200
Book Description
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 200
Book Description
Riemann's Zeta Function
Author: Harold M. Edwards
Publisher: Courier Corporation
ISBN: 9780486417400
Category : Mathematics
Languages : en
Pages : 338
Book Description
Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.
Publisher: Courier Corporation
ISBN: 9780486417400
Category : Mathematics
Languages : en
Pages : 338
Book Description
Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.
Prime Numbers and the Riemann Hypothesis
Author: Barry Mazur
Publisher: Cambridge University Press
ISBN: 1107101921
Category : Mathematics
Languages : en
Pages : 155
Book Description
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Publisher: Cambridge University Press
ISBN: 1107101921
Category : Mathematics
Languages : en
Pages : 155
Book Description
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Theory of Functions
Author: Titchmarch E. C.
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Lectures on the Riemann Zeta-Function
Author: Komaravolu Chandrasekharan (Mathematician, India, Switzerland)
Publisher:
ISBN:
Category :
Languages : en
Pages : 152
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 152
Book Description
Riemann Zeta-function
Author: Kanakanahalli Ramachandra
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 40
Book Description
Publisher:
ISBN:
Category : Functions, Zeta
Languages : en
Pages : 40
Book Description