Contents vii

Chapter 13. Prime Numbers in Arithmetic Progression 217

§13.1. Quadratic residues 217

§13.2. The proof of the Quadratic Reciprocity Law 220

§13.3. Primes in arithmetic progressions with small moduli 222

§13.4. The Primitive Divisor theorem 224

§13.5. Comments on the Primitive Divisor theorem 227

Problems on Chapter 13 228

Chapter 14. Characters and the Dirichlet Theorem 233

§14.1. Primitive roots 233

§14.2. Characters 235

§14.3. Theorems about characters 236

§14.4. L-series 240

§14.5. L(1,χ) is finite if χ is a non-principal character 242

§14.6. The nonvanishing of L(1,χ): first step 243

§14.7. The completion of the proof of the Dirichlet theorem 244

Problems on Chapter 14 247

Chapter 15. Selected Applications of Primes in Arithmetic

Progression 251

§15.1. Known results about primes in arithmetical progressions 251

§15.2. Some Diophantine applications 254

§15.3. Primes p with p − 1 squarefree 257

§15.4. More applications of primes in arithmetic progressions 259

§15.5. Probabilistic applications 261

Problems on Chapter 15 263

Chapter 16. The Index of Composition of an Integer 267

§16.1. Introduction 267

§16.2. Elementary results 268

§16.3. Mean values of λ and 1/λ 270

§16.4. Local behavior of λ(n) 273

§16.5. Distribution function of λ(n) 275

§16.6. Probabilistic results 276

Problems on Chapter 16 279

Appendix: Basic Complex Analysis Theory 281

§17.1. Basic definitions 281