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Auxiliary Polynomials in Number Theory: Cambridge Tracts in Mathematics, cartea 207

Autor David Masser
en Limba Engleză Hardback – 20 iul 2016
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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Specificații

ISBN-13: 9781107061576
ISBN-10: 1107061571
Pagini: 368
Ilustrații: 700 exercises
Dimensiuni: 158 x 236 x 28 mm
Greutate: 0.71 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:New York, United States

Cuprins

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.

Recenzii

'Several features of this book are original. First of all: the topic … Next, thanks to the unique style of the author, this book offers a pleasant reading; a number of nice jokes enable the reader to have a good time while learning high level serious mathematic … This book includes a large number of statements, proofs, ideas, problem which will be of great value for the specialists; but it should interest also any mathematician, including students, who wish to expand their knowledge and see a superb example of a topic having an surprising number of different applications in several directions.' Bulletin of the European Mathematical Society
'Instead of aiming for a polished presentation the author usually starts each chapter with simple examples and insights. This is one the book's most attractive features and could well entice students into studying the material covered.' C. Baxa, Monatshefte für Mathematik

Notă biografică


Descriere

A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.