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Sieve Methods [Minkštas viršelis]

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  • Formatas: Paperback / softback, 384 pages, aukštis x plotis x storis: 216x136x17 mm, weight: 397 g
  • Serija: Dover Books on Mathema 1.4tics
  • Išleidimo metai: 30-Sep-2011
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486479390
  • ISBN-13: 9780486479392
Kitos knygos pagal šią temą:
Sieve MethodsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 384 pages, aukštis x plotis x storis: 216x136x17 mm, weight: 397 g
  • Serija: Dover Books on Mathema 1.4tics
  • Išleidimo metai: 30-Sep-2011
  • Leidėjas: Dover Publications Inc.
  • ISBN-10: 0486479390
  • ISBN-13: 9780486479392
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780486479392.html
Raktažodžiai:
Derived from the techniques of analytic number theory, sieve theory employs methods from mathematical analysis to solve number-theoretical problems. This text by a noted pair of experts is regarded as the definitive work on the subject. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications.

"For years to come, Sieve Methods will be vital to those seeking to work in the subject, and also to those seeking to make applications," noted prominent mathematician Hugh Montgomery in his review of this volume for the Bulletin of the American Mathematical Society. The authors supply the theoretical background for the method of Jurkat-Richert and illustrate it by means of significant applications, concentrating on the "small" sieves of Brun and Selberg. Additional topics include the linear sieve, a weighted sieve, and Chen's theorem.

Derived from the techniques of analytic number theory, sieve theory employs methods from mathematical analysis to solve number-theoretical problems. This text by a noted pair of experts is regarded as the definitive work on the subject. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications.
"For years to come, Sieve Methods will be vital to those seeking to work in the subject, and also to those seeking to make applications," noted prominent mathematician Hugh Montgomery in his review of this volume for the Bulletin of the American Mathematical Society. The authors supply the theoretical background for the method of Jurkat-Richert and illustrate it by means of significant applications, concentrating on the "small" sieves of Brun and Selberg. Additional topics include the linear sieve, a weighted sieve, and Chen's theorem.


This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition.
Preface to the Dover Edition iii
Preface v
Notation xi
Errata xv
Introduction 1(11)
1 Hypotheses H and HN
1(4)
2 Sieve methods
5(3)
3 Scope and presentation
8(4)
1 The Sieve of Eratosthenes: Formulation of the General Sieve problem 12(25)
1 Introductory remarks
12(2)
2 The sequences A
14(2)
3 Basic examples
16(8)
4 The sifting set B and the sifting function S
24(6)
5 The sieve of Eratosthenes–Legendre
30(7)
2 The Combinatorial Sieve 37(60)
1 The general method
37(9)
2 Brun's pure sieve
46(6)
3 Technical preparation
52(4)
4 Brun's sieve
56(12)
5 A general upper bound O-result
68(2)
6 Sifting by a thin set of primes
70(5)
7 Further applications
75(7)
8 Fundamental Lemma
82(7)
9 Rosser's sieve
89(8)
3 The Simplest Selberg Upper Bound Method 97(33)
1 The method
97(4)
2 The case ω(d) = 1, |Rd| < or = 1
101(3)
3 Application to Σ 1 n < or = x (n, k)=1
104(1)
4 The Brun—Titchmarsh inequality
105(5)
5 The Titchmarsh divisor problem
110(3)
6 The case ω(p)= p/p-1
113(3)
7 The prime twins and Goldbach problems: explicit upper bounds
116(3)
8 The problem ap+b = p': an explicit upper bound
119(11)
4 The Selberg Upper Bound Method (continued) : O-results 130(12)
1 A lower bound for G(x, z)
130(3)
2 Applications
133(9)
5 The Selberg Upper Bound Method: Explicit Estimates 142(45)
1 A two-sided Ω2—condition
142(1)
2 Technical preparation
143(4)
3 Asymptotic formula for G(z)
147(5)
4 The main theorems
152(1)
5 Two ways of dealing with polynomial sequences {F(p)}: discussion
153(4)
6 Primes representable by polynomials
157(10)
7 Primes representable by polynomials F(p): the non-linearized approach
167(5)
8 Prime k-tuplets
172(8)
9 Primes representable by polynomials F(p): the linearized approach
180(7)
6 An Extension of Selberg's Upper Bound Method 187(17)
1 The method
187(4)
2 An upper estimate
191(2)
3 The function σx
193(4)
4 Asymptotic formula for G(ζ, z)
197(5)
5 The main result
202(2)
7 Selberg's Sieve Method (continued): A First Lower Bound 204(19)
1 Combinatorial identities
204(2)
2 An asymptotic formula for S
206(2)
3 Fundamental Lemma
208(3)
4 The function ηκ
211(2)
5 A lower bound
213(5)
6 The main result
218(5)
8 The Linear Sieve 223(18)
1 The method
223(2)
2 The functions F, f
225(3)
3 An approximate identity for the leading terms
228(3)
4 Upper and lower bounds for S
231(5)
5 The main result
236(5)
9 A Weighted Sieve: The Linear Case 241(28)
1 The method
241(6)
2 Application to the prime twins and Goldbach problems
247(5)
3 The weighted sieve in applicable form
252(4)
4 Almost-primes in intervals and arithmetic' progressions
256(3)
5 Almost-primes representable by irreducible polynomials F(n)
259(2)
6 Almost-primes representable by irreducible polynomials F(p)
261(8)
10 Weighted Sieves: The General Case 269(51)
1 The first method
269(8)
2 The first method in applicable form
277(5)
3 Almost-primes representable by polynomials
282(9)
4 The second method
291(19)
5 Almost-primes representable by polynomials
310(5)
6 Another method
315(5)
11 Chen's Theorem 320(19)
1 Introduction
320(1)
2 The weighted sieve
321(6)
3 Application of Selberg's upper sieve
327(3)
4 Transition to primitive characters
330(4)
5 Application of contour integration
334(2)
6 Application of the large sieve
336(3)
Bibliography 339(3)
References 342