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Multiplicative number theory I :classical theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512.723
書名/作者:	Multiplicative number theory I : : classical theory // Hugh L. Montgomery, Robert C. Vaughn.
作者:	Montgomery, Hugh L.,
其他作者:	Vaughan, R. C.,
面頁冊數:	1 online resource (xvii, 552 pages) : : digital, PDF file(s).
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Numbers, Prime.
ISBN:	9780511618314 (ebook)
內容註:	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 -- Appendices. A. The Riemann-Stieltjes integral; B. Bernoulli numbers and the Euler-MacLaurin summation formula; C. The gamma function; D. Topics in harmonic analysis.
摘要、提要註:	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. This 2006 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.
電子資源:	http://dx.doi.org/10.1017/CBO9780511618314

Multiplicative number theory I :classical theory /
Montgomery, Hugh L.,

Multiplicative number theory I :classical theory /Hugh L. Montgomery, Robert C. Vaughn. - 1 online resource (xvii, 552 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;97. - Cambridge studies in advanced mathematics ;105..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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 -- Appendices. A. The Riemann-Stieltjes integral; B. Bernoulli numbers and the Euler-MacLaurin summation formula; C. The gamma function; D. Topics in harmonic analysis.

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. This 2006 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.

ISBN: 9780511618314 (ebook)Subjects--Topical Terms:

587661
Numbers, Prime.

LC Class. No.: QA246 / .M75 2007

Dewey Class. No.: 512.723

Multiplicative number theory I :classical theory /
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520 $a 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. This 2006 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.
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