Prime-Detecting Sieves

Preface xi Notation xiii Chapter 1. Introduction 1 Chapter 2. The Vaughan Identity 25 Chapter 3. The Alternative Sieve 47 Chapter 4. The Rosser-Iwaniec Sieve 65 Chapter 5. Developing the Alternative Sieve 83 Chapter 6. An Upper-Bound Sieve 103 Chapter 7. Primes in Short Intervals 119 Chapter 8. The Brun-Titchmarsh Theorem on Average 157 Chapter 9. Primes in Almost All Intervals 189 Chapter 10. Combination with the Vector Sieve 201 Chapter 11. Generalizing to Algebraic Number Fields 231 Chapter 12. Variations on Gaussian Primes 265 Chapter 13. Primes of the Form x3 + 2y3 303 Chapter 14. Epilogue 335 Appendix 337 Bibliography 349 Index 361