A01=Glyn Harman
Accuracy and precision
Algebraic number
Analytic continuation
Analytic number theory
Aphorism
Arbitrarily large
Arithmetic function
Arithmetic progression
Asymptotic formula
Author_Glyn Harman
Big O notation
Bilinear form
Bombieri-Vinogradov theorem
Calculation
Carmichael number
Category=PBH
Characteristic function (probability theory)
Chen's theorem
Combination
Conjecture
Coprime integers
Dedekind domain
Diagram (category theory)
Dimension
Dirichlet character
Dirichlet L-function
Elliott-Halberstam conjecture
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Error term
Exponential function
Factorization
Fermat's Last Theorem
Fourier analysis
Fundamental theorem
Gaussian integer
Generalized Riemann hypothesis
Goldbach's conjecture
Heaviside step function
Hecke character
Ideal number
Integer
Integral domain
Iteration
L-function
Large sieve
Logarithm
Mathematics
Mean value theorem
Modular arithmetic
Multiplicative function
Multiplicative number theory
Number theory
Numerical integration
Parameter
Polynomial
Primality test
Prime factor
Prime ideal
Prime number
Prime number theorem
Quadratic function
Riemann hypothesis
Riemann zeta function
Series expansion
Siegel zero
Sieve of Eratosthenes
Square-free integer
Summation
Theorem
Twin prime
Unique factorization domain
Upper and lower bounds
Variable (mathematics)
Product details
- ISBN 9780691124377
- Weight: 595g
- Dimensions: 152 x 235mm
- Publication Date: 05 Aug 2007
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers. The subject began with Eratosthenes in antiquity, took on new shape with Legendre's form of the sieve, was substantially reworked by Ivan M. Vinogradov and Yuri V. Linnik, but came into its own with Robert C. Vaughan and important contributions from others, notably Roger Heath-Brown and Henryk Iwaniec. Prime-Detecting Sieves breaks new ground by bringing together several different types of problems that have been tackled with modern sieve methods and by discussing the ideas common to each, in particular the use of Type I and Type II information. No other book has undertaken such a systematic treatment of prime-detecting sieves. Among the many topics Glyn Harman covers are primes in short intervals, the greatest prime factor of the sequence of shifted primes, Goldbach numbers in short intervals, the distribution of Gaussian primes, and the recent work of John Friedlander and Iwaniec on primes that are a sum of a square and a fourth power, and Heath-Brown's work on primes represented as a cube plus twice a cube.
This book contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.
Glyn Harman is professor of pure mathematics at the University of London, Royal Holloway. He is the author of "Metric Number Theory", the coeditor of "Sieve Methods, Exponential Sums, and their Applications in Number Theory", and the corecipient of the Hardy-Ramanujan award for his work on primes in short intervals.
