Hindustan Book Agency 2009; 210 pp; softcover ISBN10: 8185931909 ISBN13: 9788185931906 List Price: US$38 Member Price: US$30.40 Order Code: HIN/36
 This book is an elaboration of a series of lectures given at the HarishChandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality which, when applied to the Farey dissection, will reveal connections between this inequality, the Selberg sieve and other less used notions such as pseudocharacters and the \(\Lambda_Q\)function, as well as extend these theories. One of the leading themes of these notes is the notion of socalled local models that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the BrunTichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues, and an equally novel one of the Vinogradov's Three Primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them new, like a sharp upper bound for the number of twin primes \(p\) that are such that \(p+1\) is squarefree. In the end the problem of equality in the large sieve inequality is considered, and several results in this area are also proved. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership Graduate students and research mathematicians interested in number theory. Table of Contents  Introduction
 The large sieve inequality
 An extension of the classical arithmetical theory of the large sieve
 Some general remarks on arithmetical functions
 A geometric interpretation
 Further arithmetical applications
 The Siegel zero effect
 A weighted hermitian inequality
 A first use of local models
 Twin primes and local models
 The three primes theorem
 The Selberg sieve
 Fourier expansion of sieve weights
 The Selberg sieve for sequences
 An overview
 Some weighted sequences
 Small gaps between primes
 Approximating by a local model
 Selecting other sets of moduli
 Sums of two squarefree numbers
 On a large sieve equality
 Appendix
 Notations
 References
 Index
