Auxiliary Polynomials in Number Theory
eBook - PDF

Auxiliary Polynomials in Number Theory

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Auxiliary Polynomials in Number Theory

About this book

This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals. Throughout the book, the method is explained in a 'molecular' fashion, where key ideas are introduced independently. Each application is the most elementary significant example of its kind and appears with detailed references to subsequent developments, making it accessible to advanced undergraduates as well as postgraduate students in number theory or related areas. It provides over 700 exercises both guiding and challenging, while the broad array of applications should interest professionals in fields from number theory to algebraic geometry.

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Yes, you can access Auxiliary Polynomials in Number Theory by David Masser in PDF and/or ePUB format, as well as other popular books in Mathematics & Number Theory. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Half-title
  3. Series information
  4. Title page
  5. Copyright information
  6. Table of contents
  7. Introduction
  8. 1 Prologue
  9. 2 Irrationality I
  10. 3 Irrationality II – Mahler's Method
  11. 4 Diophantine equations – Runge's Method
  12. 5 Irreducibility
  13. 6 Elliptic curves – Stepanov's Method
  14. 7 Exponential sums
  15. 8 Irrationality measures I – Mahler
  16. 9 Integer-valued entire functions I – Pólya
  17. 10 Integer-valued entire functions II – Gramain
  18. 11 Transcendence I – Mahler
  19. 12 Irrationality measures II – Thue
  20. 13 Transcendence II – Hermite–Lindemann
  21. 14 Heights
  22. 15 Equidistribution – Bilu
  23. 16 Height lower bounds – Dobrowolski
  24. 17 Height upper bounds
  25. 18 Counting – Bombieri–Pila
  26. 19 Transcendence III – Gelfond–Schneider–Lang
  27. 20 Elliptic functions
  28. 21 Modular functions
  29. 22 Algebraic independence
  30. Appendix: NƩron's square root
  31. References
  32. Index