An Introduction to Sieve Methods and Their ApplicationsCambridge University Press, 8 dec. 2005 - 224 pagini Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivating introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory. |
Cuprins
1 | 32 |
The sieve of Eratosthenes | 63 |
Bruns sieve | 80 |
Selbergs sieve | 113 |
The large sieve | 135 |
The BombieriVinogradov theorem | 156 |
The lower bound sieve | 177 |
New directions in sieve theory | 201 |
| 218 | |
| 219 | |
Alte ediții - Afișează-le pe toate
An Introduction to Sieve Methods and Their Applications Alina Carmen Cojocaru,M. Ram Murty Nu există previzualizare disponibilă - 2005 |
Termeni și expresii frecvente
a(mod A₁ apply Bombieri-Vinogradov theorem Brun-Titchmarsh theorem Brun's sieve c₁ Cauchy-Schwarz inequality Chapter character modulo choose completes the proof complex numbers composed of primes conjecture coprime d₁ d₂ deduce defined denote the number Dirichlet characters elliptic curves error term estimate irreducible polynomials Isa≤d large sieve inequality Lemma Let f Linnik log log log log x log log x)² lower bound sieve Möbius function Möbius inversion formula natural number notation number of primes number theory obtain partial summation positive constant positive integer positive real number previous exercise prime divisors prime factors prime number theorem primitive character proof of Theorem prove Re(s result Riemann hypothesis Schnirelman's Selberg's sieve set of primes Siegel-Walfisz theorem sieve method sieve of Eratosthenes sieve theory squarefree twin prime upper bound X(mod Σ μ(α Σ Σ Σμ Σμ(α ΣΣ