Book Search:  

 

 
Google full text of our books:

bookjacket

An Invitation to Modern Number Theory
Steven J. Miller & Ramin Takloo-Bighash

Book Description | Reviews
Preface [in PDF format] | Chapter 1 [in PDF format] | Chapter 3 [PDF only] | Chapter 12 [PDF only] | Chapter 15 [PDF only]

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: 4/17/2014

Questions and comments to: webmaster@press.princeton.edu
Princeton University Press

New Book E-mails
New In Print
PUP Blog
Videos/Audios
Sample Chapters
Subjects
Series
Catalogs
Textbooks
For Reviewers
Class Use
Rights
Permissions
Ordering
Recent Awards
Princeton Shorts
Freshman Reading
Princeton APPS
PUP Europe
About Us
Contact Us
Links
F.A.Q.
MATH SITE
PUP Home


Bookmark and Share