Additive Theory Of Prime Numbers

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Additive Theory Of Prime Numbers

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Author : Luogeng Hua
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-12-04

Additive Theory Of Prime Numbers written by Luogeng Hua and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-04 with Mathematics categories.

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.

Additive Number Theory The Classical Bases

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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Additive Number Theory The Classical Bases written by Melvyn B. Nathanson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

[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.

Additive Theory Of Prime Numbers

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Author :
language : en
Publisher:
Release Date : 1966

Additive Theory Of Prime Numbers written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with categories.

Additive Theory Of Prime Numbers

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Author : L. K. Hua
language : it
Publisher:
Release Date : 1965

Additive Theory Of Prime Numbers written by L. K. Hua and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.

New Developments In The Additive Theory Of Prime Numbers

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Author : Jianya Liu
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2020-02-28

New Developments In The Additive Theory Of Prime Numbers written by Jianya Liu and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-28 with Mathematics categories.

Additive Theory Of Prime Numbers

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Author : Warner Berthoff
language : en
Publisher:
Release Date : 1965

Additive Theory Of Prime Numbers written by Warner Berthoff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.

Additive Theory Of Prime Numbers

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Author : Hou Loo Keng
language : en
Publisher:
Release Date : 1953

Additive Theory Of Prime Numbers written by Hou Loo Keng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with categories.

Elementary Methods In Number Theory

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Author : Melvyn B. Nathanson
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-11

Elementary Methods In Number Theory written by Melvyn B. Nathanson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Mathematics categories.

This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion.

Additive Theory Of Prime Numbers

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Author : Lo-Keng HUA
language : en
Publisher:
Release Date : 1965

Additive Theory Of Prime Numbers written by Lo-Keng HUA and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Numbers, Prime categories.

Topics In Multiplicative Number Theory

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Author : Hugh L. Montgomery
language : en
Publisher: Springer
Release Date : 2006-11-15

Topics In Multiplicative Number Theory written by Hugh L. Montgomery and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

These notes are designed to present a survey of the present state of knowledge concerning those subjects touched upon in the last fifty pages of Davenport's Multiplicative Number Theory .