David Masser

Auxiliary Polynomials in Number Theory (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 21. Juli 2016
• Englisch
• ISBN-13: 9781316676875
• Artikelnr.: 52940914

Autorenporträt

David Masser is Emeritus Professor in the Department of Mathematics and Computer Science at the University of Basel, Switzerland. He started his career with Alan Baker, which gave him a grounding in modern transcendence theory and began his fascination with the method of auxiliary polynomials. His subsequent interest in applying the method to areas outside transcendence, which involved mainly problems of zero estimates, culminated in his works with Gisbert Wüstholz on isogeny and polarization estimates for abelian varieties, for which he was elected a Fellow of the Royal Society in 2005. This expertise proved beneficial in his more recent works with Umberto Zannier on problems of unlikely intersections, where zero estimates make a return appearance.

Inhaltsangabe

Introduction
1. Prologue
2. Irrationality I
3. Irrationality II - Mahler's method
4. Diophantine equations - Runge's method
5. Irreducibility
6. Elliptic curves - Stepanov's method
7. Exponential sums
8. Irrationality measures I - Mahler
9. Integer-valued entire functions I - Pólya
10. Integer-valued entire functions II - Gramain
11. Transcendence I - Mahler
12. Irrationality measures II - Thue
13. Transcendence II - Hermite-Lindemann
14. Heights
15. Equidistribution - Bilu
16. Height lower bounds - Dobrowolski
17. Height upper bounds
18. Counting - Bombieri-Pila
19. Transcendence III - Gelfond-Schneider-Lang
20. Elliptic functions
21. Modular functions
22. Algebraic independence
Appendix: Néron's square root
References
Index.