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Multiplicative Number Theory I: Classical Theory by Hugh L. Montgomery, Robert C. Vaughan
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Multiplicative Number Theory I: Classical Theory written by
Hugh L. Montgomery, Robert C. Vaughan .
Multiplicative number theory deals primarily with the distribution of the prime numbers, but also with the asymptotic behavior of prime-related functions such as the number-of-divisors function. The present work deals with the classical theory in the sense that most of the results were known before 1960. Most of the items covered are part of analytic number theory and the theory of the Riemann zeta function and the L-functions. In addition to the analytic theory the book includes classical estimates of Dirichlet, Chebyshev, and Mertens, as well as some coverage of combinatorial sieves and the Selberg sieve. A second volume is planned that will focus on more delicate estimates, exponential sums, and sieve methods.
The unique feature of the book is its exercises: they cover hundreds of research results (with references), usually just stated but sometimes with hints or a step by step breakdown. The body of the text follows the mainstream and only hits the main results, but gives the student enough background to work on the exercises.
The book is clearly written and includes enough background information to be used for individual study. Some earlier works that have a similar flavor but are less comprehensive are A. E. Ingham's The Distribution of Prime Numbers (Cambridge Mathematical Library) and Harold Davenport's Multiplicative Number Theory
Book Detail :-
Title: Multiplicative Number Theory I: Classical Theory
Author(s): Hugh L. Montgomery, Robert C. Vaughan
Publisher: Cambridge University Press
Series: Cambridge Studies in Advanced Mathematics
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About Author :-
The author Hugh Lowell Montgomery (born, 1944) is an American mathematician, working in the fields of analytic number theory and mathematical analysis. As a Marshall scholar, Montgomery earned his Ph.D. from the University of Cambridge. For many years, Montgomery has been teaching at the University of Michigan.
He is best known for Montgomery's pair correlation conjecture, his development of the large sieve methods and for co-authoring (with Ivan M. Niven and Herbert Zuckerman) one of the standard introductory number theory texts, An Introduction to the Theory of Numbers, now in its fifth edition (ISBN 0471625469). In 2012 he became a fellow of the American Mathematical Society.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Exploring the Riemann Zeta Function by Hugh Montgomery, Ashkan Nikeghbali, Michael Rassias
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• Download PDF Multiplicative Number Theory I: Classical Theory by Hugh L. Montgomery, Robert C. Vaughan
• Download PDF Interface between Analytic Number Theory & Harmonic Analysis by Hugh L. Montgomery
• Download PDF An Introduction to the Theory of Numbers, 5E by Ivan Niven, Herbert Zuckerman, Hugh Montgomery
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Book Contents :-
Ten Lectures on the Interface between Analytic Number Theory & Harmonic Analysis written by
Hugh L. Montgomery
cover the following topics.
1. Dirichlet series: I
2. The elementary theory of arithmetic functions
3. Principles and first examples of sieve methods
4. Primes in arithmetic progressions: I
5. Dirichlet series: II
6. The Prime Number Theorem
7. Applications of the Prime Number Theorem
8. Further discussion of the Prime Number Theorem
9. Primitive characters and Gauss sums
10. Analytic properties of the zeta function and L-functions
11. Primes in arithmetic progressions: II
12. Explicit formulæ
13. Conditional estimates
15. Oscillations of error terms
APPENDIX A The Riemann–Stieltjes integral
APPENDIX B Bernoulli numbers and the Euler–MacLaurin summation formula
APPENDIX C The gamma function
APPENDIX D Topics in harmonic analysis
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