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  3. Logarithmic Forms and Diophantine Geometry
  • Cited by 31
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    • Publisher:
      Cambridge University Press
      Publication date:
      November 2009
      January 2008
      ISBN:
      9780511542862
      9780521882682
      DOI:
      https://doi.org/10.1017/CBO9780511542862
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.43kg, 208 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Number Theory
      Series:
      New Mathematical Monographs (9)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory
    Series:
    New Mathematical Monographs (9)
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    Book description

    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.

    Reviews

    "This book gives the necessary intuitive background to study the original journal articles of Baker, Masser, Wüstholz and others..."
    Yuri Bilu, Mathematical Reviews

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