Arithmetical Aspects of the Large Sieve Inequality

Description

Front Matter....Pages i-x Introduction....Pages 1-5 The large sieve inequality....Pages 7-15 An extension of the classical arithmetical theory of the large sieve....Pages 17-26 Some general remarks on arithmetical functions....Pages 27-29 A geometrical interpretation....Pages 31-38 Further arithmetical applications....Pages 39-49 The Siegel zero effect....Pages 51-60 A weighted hermitian inequality....Pages 61-62 A first use of local models....Pages 63-74 Twin primes and local models....Pages 75-81 The three primes theorem....Pages 83-94 The Selberg sieve....Pages 95-104 Fourier expansion of sieve weights....Pages 105-109 The Selberg sieve for sequences....Pages 111-117 An overview....Pages 119-120 Some weighted sequences....Pages 121-127 Small gaps between primes....Pages 129-137 Approximating by a local model....Pages 139-142 Selecting other sets of moduli....Pages 143-145 Sums of two squarefree numbers....Pages 147-157 On a large sieve equality....Pages 159-176 Appendix....Pages 177-186 Back Matter....Pages 187-201