Chapters in this book

1. Frontmatter i
2. Contents vii
3. Foreword xi
4. Preface xiii
5. Notation xix
6. PART 1. BASIC NUMBER THEORY
7. Chapter 1. Mod p Arithmetic, Group Theory and Cryptography 1
8. Chapter 2. Arithmetic Functions 29
9. Chapter 3. Zeta and L-Functions 47
10. Chapter 4. Solutions to Diophantine Equations 81
11. PART 2. CONTINUED FRACTIONS AND APPROXIMATIONS
12. Chapter 5. Algebraic and Transcendental Numbers 109
13. Chapter 6. The Proof of Roth’s Theorem 137
14. Chapter 7. Introduction to Continued Fractions 158
15. PART 3. PROBABILISTIC METHODS AND EQUIDISTRIBUTION
16. Chapter 8. Introduction to Probability 191
17. Chapter 9. Applications of Probability: Benford’s Law and Hypothesis Testing 216
18. Chapter 10. Distribution of Digits of Continued Fractions 231
19. Chapter 11. Introduction to Fourier Analysis 255
20. Chapter 12. {n^k∝} and Poissonian Behavior 278
21. PART 4. THE CIRCLE METHOD
22. Chapter 13. Introduction to the Circle Method 303
23. Chapter 14. Circle Method: Heuristics for Germain Primes 326
24. PART 5. RANDOM MATRIX THEORY AND L-FUNCTIONS
25. Chapter 15. From Nuclear Physics to L-Functions 359
26. Chapter 16. Random Matrix Theory: Eigenvalue Densities 391
27. Chapter 17. Random Matrix Theory: Spacings between Adjacent Eigenvalues 405
28. Chapter 18. The Explicit Formula and Density Conjectures 421
29. Appendix A. Analysis Review 439
30. Appendix B. Linear Algebra Review 455
31. Appendix C. Hints and Remarks on the Exercises 463
32. Appendix D. Concluding Remarks 475
33. Bibliography 476
34. Index 497