TABLE OF CONTENTS: Foreword xi
Preface xiii
Notation xix
PART 1. BASIC NUMBER THEORY 1
Chapter 1. Mod p Arithmetic, Group Theory and Cryptography 3
Chapter 2. Arithmetic Functions 29
Chapter 3. Zeta and L-Functions 47
Chapter 4. Solutions to Diophantine Equations 81
PART 2. CONTINUED FRACTIONS AND APPROXIMATIONS 107
Chapter 5. Algebraic and Transcendental Numbers 109
Chapter 6. The Proof of Roth's Theorem 137
Chapter 7. Introduction to Continued Fractions 158
PART 3. PROBABILISTIC METHODS AND EQUIDISTRIBUTION 189
Chapter 8. Introduction to Probability 191
Chapter 9. Applications of Probability: Benford's Law and Hypothesis Testing 216
Chapter 10. Distribution of Digits of Continued Fractions 231
Chapter 11. Introduction to Fourier Analysis 255
Chapter 12. f n k g and Poissonian Behavior 278
PART 4. THE CIRCLE METHOD 301
Chapter 13. Introduction to the Circle Method 303
Chapter 14. Circle Method: Heuristics for Germain Primes 326
PART 5. RANDOM MATRIX THEORY AND L-FUNCTIONS 357
Chapter 15. From Nuclear Physics to L-Functions 359
Chapter 16. Random Matrix Theory: Eigenvalue Densities 391
Chapter 17. Random Matrix Theory: Spacings between Adjacent Eigenvalues 405
Chapter 18. The Explicit Formula and Density Conjectures 421
Appendix A. Analysis Review 439
Appendix B. Linear Algebra Review 455
Appendix C. Hints and Remarks on the Exercises 463
Appendix D. Concluding Remarks 475
Bibliography 476
Index 497
Return to Book Description File created: 4/25/2013 | 
