Arithmetical Aspects of the Large Sieve Inequality

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