An invitation to modern number theory /

In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experime...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Miller, Steven J., 1974-
Otros Autores: Takloo-Bighash, Ramin
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, ©2006.
Temas:
Number theory.
Théorie des nombres.
MATHEMATICS > Number Theory.
Number theory
Zahlentheorie
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • PART 1. BASIC NUMBER THEORY
  • 1. Mod p Arithmetic, Group Theory and Cryptography
  • 2. Arithmetic Functions
  • 3. Zeta and L-Functions
  • 4. Solutions to Diophantine Equations
  • PART 2. CONTINUED FRACTIONS AND APPROXIMATIONS
  • 5. Algebraic and Transcendental Numbers
  • 6. The Proof of Roth's Theorem
  • 7. Introduction to Continued Fractions
  • PART 3. PROBABILISTIC METHODS AND EQUIDISTRIBUTION
  • 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. f n k g and Poissonian Behavior
  • PART 4. THE CIRCLE METHOD
  • 13. Introduction to the Circle Method
  • 14. Circle Method: Heuristics for Germain Primes
  • PART 5. RANDOM MATRIX THEORY AND L-FUNCTIONS
  • 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.

Ejemplares similares