Multiplicative Number Theory - Volume 1

Classical Theory

Hugh L. Montgomery, Robert Vaughan - Collection Cambridge Studies in Advanced Mathematics

584 pages, parution le 20/11/2006

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Résumé

Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. The text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.

Large collection of stimulating problems associated with each section
Extensive references to both historical background and further development of subject
Based extensively on the material used successfully at the University of Michigan, Imperial College London, and Penn State University

Sommaire

Dirichlet series-I
The elementary theory of arithmetic functions
Principles and first examples of sieve methods
Primes in arithmetic progressions-I
Dirichlet series-II
The prime number theorem
Applications of the prime number theorem
Further discussion of the prime number theorem
Primitive characters and Gauss sums
Analytic properties of the zeta function and L-functions
Primes in arithmetic progressions-II
Explicit formulae
Conditional estimates
Zeros
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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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Hugh L. Montgomery, Robert Vaughan
Collection	Cambridge Studies in Advanced Mathematics
Parution	20/11/2006
Nb. de pages	584
Format	16 x 23,5
Couverture	Relié
Poids	1020g
Intérieur	Noir et Blanc
EAN13	9780521849036
ISBN13	978-0-521-84903-6