Contents ix
§6. An application to the Goldbach problem 196
Notes 201
Exercises 202
Chapter 7. An Elementary Proof of the Prime Number Theorem 213
§1. Introduction 214
§2. Chebyshev’s theorems revisited 217
§3. Proof of Selberg’s fundamental formula 221
§4. Removing the explicit appearance of primes 224
§5. Nevanlinna’s finishing strategy 231
Notes 235
Exercises 237
Chapter 8. Perfect Numbers and their Friends 247
§1. Introduction and overview 248
§2. Proof of Dickson’s finiteness theorem 253
§3. How rare are odd perfect numbers? 255
§4. The distribution function of σ(n)/n 259
§5. Sociable numbers 263
Notes 267
Exercises 269
References 279
Index 301
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