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.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Information
Table of contents
- Cover
- Half-title
- Series information
- Title page
- Copyright information
- Table of contents
- Introduction
- 1 Prologue
- 2 Irrationality I
- 3 Irrationality II ā Mahler's Method
- 4 Diophantine equations ā Runge's Method
- 5 Irreducibility
- 6 Elliptic curves ā Stepanov's Method
- 7 Exponential sums
- 8 Irrationality measures I ā Mahler
- 9 Integer-valued entire functions I ā Pólya
- 10 Integer-valued entire functions II ā Gramain
- 11 Transcendence I ā Mahler
- 12 Irrationality measures II ā Thue
- 13 Transcendence II ā HermiteāLindemann
- 14 Heights
- 15 Equidistribution ā Bilu
- 16 Height lower bounds ā Dobrowolski
- 17 Height upper bounds
- 18 Counting ā BombieriāPila
- 19 Transcendence III ā GelfondāSchneiderāLang
- 20 Elliptic functions
- 21 Modular functions
- 22 Algebraic independence
- Appendix: NƩron's square root
- References
- Index
