Last edited by Kejora
Saturday, August 1, 2020 | History

2 edition of Additive theory of prime numbers found in the catalog.

Lo-kГЄng Hua

# Additive theory of prime numbers

## by Lo-kГЄng Hua

Written in English

Subjects:
• Numbers, Prime

• Edition Notes

The Physical Object ID Numbers Series Translations of mathematical monographs -- v. 13 Pagination 190p. Number of Pages 190 Open Library OL14806051M

I am especially interested in multiplicative and probabilistic aspects of number theory, the anatomy of integers and permutations, sieve methods, and additive combinatorics. In , I published a book on the distribution of prime numbers. One of the main results in additive number theory is the solution to Waring's problem. History Precursors. Much of analytic number theory was inspired by the prime number theorem. Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for any real number x. For example, π(10) = 4 because there are.

P. Erdős, Some problems in number theory, in Computers in Number Theory, Academic Press, London & New York, , – Google Scholar P. Erdős & H. Heilbronn, On the addition of residue clesses mod p, Acta Arith., 9 () – Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A.

Number theory - Number theory - Euclid: By contrast, Euclid presented number theory without the flourishes. He began Book VII of his Elements by defining a number as “a multitude composed of units.” The plural here excluded 1; for Euclid, 2 was the smallest “number.” He later defined a prime as a number “measured by a unit alone” (i.e., whose only proper divisor is 1), a composite. New Developments In The Additive Theory Of Prime Numbers 作者: Jianya Liu; Tao Zhan; Liu, Jianya 页数: 定价: 元 ISBN: 豆瓣评分.

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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 Cited by:   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. Buy Additive Theory of Prime Numbers by Lo-keng Hua online at Alibris. We have new and used copies available, in 1 editions - starting at \$ Shop now.

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.

Additive Theory of Prime Numbers by L. Hua,available at Book Depository with free delivery worldwide. New Developments in the Additive Theory of Prime Additive theory of prime numbers book by Jianya Liu,available at Book Depository with free delivery worldwide.

Abstract. The undecidability of the additive theory of prime numbers (with identity) as well as the theory Th(N, +, n ↦ p [TeX:] _n), where pn denotes the (n + 1)-th prime, are open a first part, we show the undecidability of Th(N, +, n ↦ nf(n)) where f is a good approximation of the enumeration n ↦ p [TeX:] _n /n.

In a second part, as a possible approach, we extend the. 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. 4 Number Theory I: Prime Numbers Number theory is the mathematical study of the natural numbers, the positive whole numbers such as 2, 17, and Despite their ubiquity and apparent sim-plicity, the natural integers are chock-full of beautiful ideas and open problems.

A primary focus of number theory is the study of prime numbers, which can be. Additive prime number theory Additive prime number theoryis the study of additive patterns in the prime numbers 2;3;5;7; Examples of additive patterns includetwins p;p + 2, arithmetic progressions a;a + r;;a + (k 1)r, and prime gaps pn+1 pn.

Many open problems regarding these patterns still remain, but there has been some recent progress. Classical problems in additive number theory include: the representation of a number as a sum of four squares, nine cubes, etc.

(cf. Waring problem); the representation of a given number as a sum of not more than three prime numbers (cf. Goldbach problem); and the representation of a given number as a sum of one prime number and two squares (cf.

Additive Theory of Prime Numbers 作者: Hua, Lo-Keng/ Ng, N. (TRN) 出版社: Amer Mathematical Society 定价: 46 装帧: HRD ISBN: 豆瓣评分. Buy a cheap copy of Additive Theory of Prime Numbers book by Lo-Keng Hua. Free shipping over \$ Additive theory of prime numbers.

[Lo-kêng Hua] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Contacts Search for a Library. Create Book: All Authors / Contributors: Lo-kêng Hua. Find more information about: OCLC Number. Text. A positive integer n is called weakly prime-additive if n has at least two distinct prime divisors and there exist distinct prime divisors p 1,p t of n and positive integers α 1,α t such that n = p 1 α 1 + ⋯ + p t α is clear that t ≥Erdős and Hegyvári proved that, for any prime p, there exist infinitely many weakly prime-additive numbers with t = 3.

Let π(x) be the prime-counting function that gives the number of primes less than or equal to x, for any real number example, π(10) = 4 because there are four prime numbers (2, 3, 5 and 7) less than or equal to The prime number theorem then states that x / log x is a good approximation to π(x) (where log here means the natural logarithm), in the sense that the limit of the.

Abstract. We discuss the solubility of the ternary equations x 2 +y 3 +z k = n for an integer k with 3 ≤ k ≤ 5 and large integers n, where two of the variables are primes, and the remaining one is an almost prime. We are also concerned with related quaternary problems. As usual, an integer with at most r prime factors is called a P shall show, amongst other things, that for.

Prime numbers, the building blocks of integers, have been studied extensively over the centuries. Being able to present an integer uniquely as product of primes is the main reason behind the whole theory of numbers and behind the interesting results in this theory.

One of the most fundamental methods in the study of Additive Prime Num-ber Theory is the Circle Method. The Circle Method was rst conceptualized in Asymptotic formulae in combinatory analysis  by G.H.

Hardy and S. Ra-manujan inapproximately 20 years after the development of the prime number theorem. 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. : New Developments In The Additive Theory Of Prime Numbers (): Jianya Liu, Tao Zhan: BooksCited by: 3.In Additive Number Theory we study subsets of integers and their behavior under addition.

Deﬁnition: A +B:={a +b|a ∈ A,b ∈ B}. Example: A ={7,13,15,22}; Goldbach conjecture: If P is the set of all prime numbers, then P +P is the set of all even integers. Introduction Inverse Problems: Here we start with h-fold sumhA and.Analytic number theory: additive problems.

Twin prime. Brun's constant; Cousin prime; Prime triplet; Prime quadruplet; Sexy prime; Sophie Germain prime; Cunningham chain; Goldbach's conjecture. Goldbach's weak conjecture; Second Hardy–Littlewood conjecture; Hardy–Littlewood circle method; Schinzel's hypothesis H; Bateman–Horn conjecture.