Auxiliary polynomials in number theory 1st Edition by David Masser ISBN 1107061571 978-1107061576

Auxiliary polynomials in number theory 1st Edition by David Masser – Ebook PDF Instant Download/Delivery: 1107061571, 978-1107061576

Full download Auxiliary polynomials in number theory 1st Edition after payment

Product details:

ISBN 10: 1107061571 

ISBN 13: 978-1107061576

Author: David Masser

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.

Table of contents:

1. Introduction

2. Prologue

3. Irrationality I

4. Irrationality II – Mahler’s Method

5. Diophantine Equations – Runge’s Method

6. Irreducibility

7. Elliptic Curves – Stepanov’s Method

8. Exponential Sums

9. Irrationality Measures I – Mahler

10. Integer-Valued Entire Functions I – Pólya

11. Integer-Valued Entire Functions II – Gramain

12. Transcendence I – Mahler

13. Irrationality Measures II – Thue

14. Transcendence II – Hermite–Lindemann

15. Heights

16. Equidistribution – Bilu

17. Height Lower Bounds – Dobrowolski

18. Height Upper Bounds

19. Counting – Bombieri–Pila

20. Transcendence III – Gelfond–Schneider–Lang

21. Elliptic Functions

22. Modular Functions

23. Algebraic Independence

24. Appendix: Néron’s Square Root

25. References

26. Index

People also search for:

are numbers polynomials
    
are polynomials algebra 1 or 2
    
are polynomials algebra 2
    
are polynomials important
    
can a number be a polynomial

Tags: David Masser, Auxiliary polynomials, in number theory