Applications of sieve methods to the theory of numbers / C. HooleyType de document : MonographieCollection : Cambridge tracts in mathematics, 70Langue : anglais.Pays: Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 1976Description : 1 vol. (XIV-122 p.) ; 22 cmISBN: 9780521209151.ISSN: 0950-6284.Bibliographie : Bibliogr. p. 119-122.Sujet MSC : 11N35, Multiplicative number theory, Sieves
11Mxx, Number theory - Zeta and L-functions: analytic theory
11P05, Additive number theory; partitions, Waring's problem and variants
11P32, Additive number theory; partitions, Goldbach-type theorems; other additive questions involving primesEn-ligne : Zentralblatt | MathSciNet Item type: Monographie
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The aim of the present book is to give interesting and difficult examples of applications of sieve methods to deep problems in number theory. Generally in handling these problems the power of the sieve method has to be increased by combination with other techniques, such as Dirichlet series, complex integration, estimates of exponential sums, or by using results from algebraic number theory, from lattice point theory, from prime number theory, and often it is difficult to see how to transform the problem into a form that allows the application of some sieve method. The choice of topics treated in the book is strongly influenced by the research of the author. The book is designed for readers having merely a general background in the theory of numbers. The text is clear and concise, and the ideas lying behind are well sketched; but in spite of the excellent presentation the reading of the book is not too easy.
The first chapter gives an elegant survey of sieve methods, which are needed in the following chapters of the book. There is a description of combinatorial identities, of Selberg's upper bound sieve, of the lower bound sieve and of the large sieve; the so-called "enveloping sieve'' is treated in detail in Chapter V. (MathSciNet)
Bibliogr. p. 119-122
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