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 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.
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 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 Number Theory Of Polynomials Over A Finite Field
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Author : Gove W. Effinger
language : en
Publisher:
Release Date : 1991
Additive Number Theory Of Polynomials Over A Finite Field written by Gove W. Effinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This book helps gather the sum of additive number theory.
Combinatorial And Additive Number Theory
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Author : Melvyn B. Nathanson
language : en
Publisher: Springer
Release Date : 2014-10-18
Combinatorial And Additive Number Theory written by Melvyn B. Nathanson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-18 with Mathematics categories.
This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.
Elementary Theory Of Numbers
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Author : W. Sierpinski
language : en
Publisher: Elsevier
Release Date : 1988-02-01
Elementary Theory Of Numbers written by W. Sierpinski and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-02-01 with Mathematics categories.
Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised. The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers.
Number Theory
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Author : W Narkiewicz
language : en
Publisher: World Scientific Publishing Company
Release Date : 1984-02-01
Number Theory written by W Narkiewicz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-02-01 with Mathematics categories.
The aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory. The author tries to show the connection between number theory and other branches of mathematics with the resultant tools adopted in the book ranging from algebra to probability theory, but without exceeding the undergraduate students who wish to be acquainted with number theory, graduate students intending to specialize in this field and researchers requiring the present state of knowledge.
The Prime Number Theorem
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Author : G. J. O. Jameson
language : en
Publisher: Cambridge University Press
Release Date : 2003-04-17
The Prime Number Theorem written by G. J. O. Jameson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-17 with Mathematics categories.
At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material.
Introduction To Modern Prime Number Theory
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Author : T. Estermann
language : en
Publisher: Cambridge University Press
Release Date : 2011-08-11
Introduction To Modern Prime Number Theory written by T. Estermann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.
This 1952 book attempts to prove the Vinogradov-Goldbach theorem: that every sufficiently large odd number is the sum of three primes.