Divisors

Contents......Page 7
Preface......Page 11
Notation......Page 15
Goto 14 /FitH 555.2 Sums of multiplicative functions......Page 17
Goto 14 /FitH 555.4 Local distributions of prime factors and Poisson variables......Page 20
Goto 14 /FitH 555.5 A general principle......Page 22
Notes on Chapter 0......Page 25
Exercises on Chapter 0......Page 27
1.1 The law of the iterated logarithm......Page 30
1.2 The normal size of p;(n) and d;(n)......Page 37
Notes on Chapter 1......Page 40
Exercises on Chapter 1......Page 41
2.1 Introduction......Page 43
2.2 Statement of results concerning H(x, y, z)......Page 45
2.3 More applications......Page 47
2.4 Proof of Theorem 22......Page 50
2.5 Proof of Theorem 21(i) - small z......Page 54
2.6 Proof of Theorem 21 (ii), (iii) - upper bounds......Page 56
2.7 Proof of Theorem 21 (ii), (iii) - lower bounds......Page 57
2.8 Proof of Theorem 21(iv) - large z......Page 62
Notes on Chapter 2......Page 64
Exercises on Chapter 2......Page 65
3.2 A p.p. upper bound for |i(n,0)|......Page 68
3.3 Ratios of divisors......Page 72
3.4 Average orders......Page 73
Notes on Chapter 3......Page 78
Exercises on Chapter 3......Page 80
4.2 T and U - preliminary matters......Page 81
4.3 T and U - average orders......Page 83
4.4 The normal orders of log T and log U......Page 90
4.5 The function T(n,0)/i(n)......Page 95
4.6 Erdos' function T + (n)......Page 99
4.7 Hooley's function A(n)......Page 105
Notes on Chapter 4......Page 108
Exercises on Chapter 4......Page 109
5.1 Introduction and results......Page 111
5.2 Proof of Theorem 50......Page 115
5.3 Proof of Theorem 51......Page 120
5.4 A p.p. upper bound for the A-function......Page 127
Notes on Chapter 5......Page 134
Exercises on Chapter 5......Page 136
6.1 Introduction......Page 137
6.2 Lower bounds......Page 138
6.3 The critical interval......Page 139
6.4 Technical preparation......Page 140
6.5 Iteration inequalities......Page 142
6.6 Small y - the lower bound for A~......Page 143
6.7 Fourier transforms - initial treatment......Page 144
6.8 Fourier transforms - an upper bound for Ar+......Page 148
Notes on Chapter 6......Page 152
Exercises on Chapter 6......Page 154
7.1 Introduction......Page 155
7.2 Notation. The fundamental lemma......Page 156
7.3 First variant - differential inequalities......Page 162
7.4 Second variant - double induction......Page 166
Notes on Chapter 7......Page 172
Exercises on Chapter 7......Page 173
Appendix: Distribution functions......Page 174
Bibliography......Page 177
Index......Page 181