An Invitation to Modern Number Theory

Title
Contents
Foreword
Preface
Notation
1. Mod p Arithmetic, Group Theory and Cryptography
2. Arithmetic Functions
3. Zeta and L-Functions
4. Solutions to Diophantine Equations
5. Algebraic and Transcendental Numbers
6. The Proof of Roth’s Theorem
7. Introduction to Continued Fractions
8. Introduction to Probability
9. Applications of Probability: Benford’s Law and Hypothesis Testing
10. Distribution of Digits of Continued Fractions
11. Introduction to Fourier Analysis
12. {n^k alpha} and Poissonian Behavior
13. Introduction to the Circle Method
14. Circle Method: Heuristics for Germain Primes
15. From Nuclear Physics to L-Functions
16. Random Matrix Theory: Eigenvalue Densities
17. Random Matrix Theory: Spacings between Adjacent Eigenvalues
18. The Explicit Formula and Density Conjectures
Appendix A. Analysis Review
Appendix B. Linear Algebra Review
Appendix C. Hints and Remarks on the Exercises
Appendix D. Concluding Remarks
Bibliography
Index