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Table of contents

  1. Front Matter
    Pages i-xiii
  2. Timothy D. Browning
    Pages 1-15
  3. Timothy D. Browning
    Pages 17-46
  4. Timothy D. Browning
    Pages 47-62
  5. Timothy D. Browning
    Pages 63-82
  6. Timothy D. Browning
    Pages 83-97
  7. Timothy D. Browning
    Pages 99-111
  8. Timothy D. Browning
    Pages 113-122
  9. Timothy D. Browning
    Pages 123-149
  10. Back Matter
    Pages 151-160

About this book

Keywords

Diophantine equation Manin conjectures del Pezzo surfaces number theory uniform bounds

Authors and affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUK

Bibliographic information

  • Book Title Quantitative Arithmetic of Projective Varieties
  • Authors Timothy D. Browning
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0346-0129-0
  • Copyright Information Birkhäuser Basel 2009
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0346-0128-3
  • eBook ISBN 978-3-0346-0129-0
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XIII, 160
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
    Differential Geometry
  • Buy this book on publisher's site
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Reviews

From the reviews:

“The book under review considers the distribution of integral or rational points of bounded height on (projective) algebraic varieties. … well-written and well-organized. … Introductory material is discussed when appropriate, motivation and context are provided when necessary, and there are even small sets of exercises at the end of every chapter, making the book suitable for self or guided study … .” (Felipe Zaldivar, The Mathematical Association of America, January, 2010)

“The most important feature of the book is the way it presents the geometric and analytic aspects of the theory on a unified equal footing. The interface between these two fields has been a very productive subject in recent years, and this book is likely to be of considerable value to anyone, graduate student and up, interested in this area.” (Roger Heath-Brown, Zentralblatt MATH, Vol. 1188, 2010)

“The book … is focused on exposing how tools rooted in analytic number theory can be used to study quantitative problems in Diophantine geometry, by focusing on the Manin conjectures, the dimension growth conjecture, and the Hardy-Littlewood circle method. … book is clear, concise, and well written, and as such is highly recommended to a beginning graduate student looking for direction in pure mathematics or number theory. … includes a number of interesting and accessible exercises at the end of each of the eight chapters.”­­­ (Robert Juricevic, Mathematical Reviews, Issue 2010 i)