Arithmetic Tales
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Author |
: Olivier Bordellès |
Publisher |
: Springer Nature |
Total Pages |
: 782 |
Release |
: 2020-11-26 |
ISBN-10 |
: 9783030549466 |
ISBN-13 |
: 3030549461 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Arithmetic Tales by : Olivier Bordellès
This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Author |
: Olivier Bordellès |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 569 |
Release |
: 2012-05-31 |
ISBN-10 |
: 9781447140962 |
ISBN-13 |
: 1447140966 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Arithmetic Tales by : Olivier Bordellès
Number theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included. Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it will appeal to a wide target group including upper level undergraduates, doctoral and masters level students.
Author |
: Olivier Bordellès |
Publisher |
: Springer |
Total Pages |
: 782 |
Release |
: 2020-11-27 |
ISBN-10 |
: 3030549453 |
ISBN-13 |
: 9783030549459 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Arithmetic Tales by : Olivier Bordellès
This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.
Author |
: |
Publisher |
: |
Total Pages |
: 804 |
Release |
: 1900 |
ISBN-10 |
: NYPL:33433075984652 |
ISBN-13 |
: |
Rating |
: 4/5 (52 Downloads) |
Synopsis Annual Report by :
Author |
: Maria Edgeworth |
Publisher |
: |
Total Pages |
: 478 |
Release |
: 1856 |
ISBN-10 |
: NYPL:33433082229745 |
ISBN-13 |
: |
Rating |
: 4/5 (45 Downloads) |
Synopsis Tales and Novels by : Maria Edgeworth
Author |
: Maria Edgeworth |
Publisher |
: |
Total Pages |
: 456 |
Release |
: 1850 |
ISBN-10 |
: BML:37001101596992 |
ISBN-13 |
: |
Rating |
: 4/5 (92 Downloads) |
Synopsis IIlustrated Tales for Children by : Maria Edgeworth
Author |
: L. Valentine |
Publisher |
: BoD – Books on Demand |
Total Pages |
: 662 |
Release |
: 2023-11-15 |
ISBN-10 |
: 9783368843854 |
ISBN-13 |
: 3368843850 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Maria Edgeworth's Moral and Popular Tales by : L. Valentine
Reprint of the original, first published in 1874.
Author |
: |
Publisher |
: |
Total Pages |
: 1394 |
Release |
: 1911 |
ISBN-10 |
: UCAL:B4172269 |
ISBN-13 |
: |
Rating |
: 4/5 (69 Downloads) |
Synopsis The Publishers Weekly by :
Author |
: |
Publisher |
: |
Total Pages |
: 294 |
Release |
: 1813 |
ISBN-10 |
: IBNN:BNVA1001540518 |
ISBN-13 |
: |
Rating |
: 4/5 (18 Downloads) |
Synopsis Moral Tales by Miss Edgeworth. In Three Volumes by :
Author |
: William George Bruce |
Publisher |
: |
Total Pages |
: 464 |
Release |
: 1895 |
ISBN-10 |
: UOM:39015084571028 |
ISBN-13 |
: |
Rating |
: 4/5 (28 Downloads) |
Synopsis The American School Board Journal by : William George Bruce