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Author: Luogeng Hua
Publisher: American Mathematical Soc.
ISBN: 0821849425
Category : Mathematics
Languages : en
Pages : 206
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Book Description
Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Author: Luogeng Hua
Publisher: American Mathematical Soc.
ISBN: 0821849425
Category : Mathematics
Languages : en
Pages : 206
Get Book
Book Description
Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 190
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Book Description
Author: Jianya Liu
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789812775924
Category : Mathematics
Languages : en
Pages : 200
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Book Description
Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
ISBN: 1475738455
Category : Mathematics
Languages : en
Pages : 350
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Book Description
[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.
Author: Melvyn B. Nathanson
Publisher:
ISBN: 9781475738469
Category :
Languages : en
Pages : 362
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Book Description
Author: János Pintz
Publisher: Springer
ISBN: 3319927779
Category : Mathematics
Languages : en
Pages : 217
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Book Description
This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.
Author: Gove W. Effinger
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 184
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Book Description
This book helps gather the sum of additive number theory.
Author: Melvyn Bernard Nathanson
Publisher:
ISBN:
Category :
Languages : en
Pages : 293
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Book Description
Author: Benjamin Fine
Publisher: Springer Science & Business Media
ISBN: 0817645411
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises make it ideal for self study and classroom use.
Author: Albert Edward Ingham
Publisher: Cambridge University Press
ISBN: 9780521397896
Category : Mathematics
Languages : en
Pages : 140
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Book Description
Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
