Other available formats:
Looking for an examination copy?
If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact email@example.com providing details of the course you are teaching.
There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the André-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.Read more
- Destined to be the definitive reference on effective methods in Diophantine geometry
- First version in book form of important developments of the past twenty-five years on multiplicity estimates on group varieties
- Much original material including detailed exposition of the fundamental analytic subgroup theorem and its applications
Reviews & endorsements
"This book gives the necessary intuitive background to study the original journal articles of Baker, Masser, Wüstholz and others..."
Yuri Bilu, Mathematical Reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: February 2008
- format: Hardback
- isbn: 9780521882682
- length: 208 pages
- dimensions: 235 x 161 x 16 mm
- weight: 0.43kg
- contains: 1 b/w illus.
- availability: In stock
Table of Contents
Preface. 1. Transcendence origins
2. Logarithmic forms
3. Diophantine problems
4. Commutative algebraic groups
5. Multiplicity estimates
6. The analytic subgroup theorem
7. The quantitative theory
8. Further aspects of Diophantine geometry
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×