This book is concerned with counting rational points of bounded height on projective algebraic varieties. This is a fertile and vibrant topic that lies at the interface of analytic number theory and Diophantine geometry. The goal of the book is to give a systematic account of the field with an emphasis on the role that analytic number theory has to play in its development. Winner of theFerran Sunyer i Balaguer Prize 2009 First attempt to systematically survey the range of available tools from analytic number theory that can be applied to study the density of rational points on projective varieties. Designed to rapidly guide the reader to the many areas of ongoing research in the domain Provides an extensive bibliography INDICE: Preface.- 1. Introduction.- 2. The Manin Conjectures.- 3. The Dimension Growth Conjecture.- 4. Uniform Bounds for Curves and Surfaces.- 5. A1 Del Pezzo Surface of Degree 6.- 6. D4 Del Pezzo Surface of Degree 3.- 7. Siegel's Lemma and Non-singular Surfaces.- 8. The Hardy-Littlewood Circle Method.- Bibliography.- Index.
- ISBN: 978-3-0346-0128-3
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 170
- Fecha Publicación: 01/11/2009
- Nº Volúmenes: 1
- Idioma: Inglés