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  3. The Algorithmic Resolution of Diophantine Equations
  • Cited by 70
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2013
      November 1998
      ISBN:
      9781107359994
      9780521641562
      9780521646338
      DOI:
      https://doi.org/10.1017/CBO9781107359994
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.471kg, 260 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.39kg, 260 Pages
      • Subjects:
      Mathematics (general), Mathematics, Number Theory
      Series:
      London Mathematical Society Student Texts (41)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory
    Series:
    London Mathematical Society Student Texts (41)
    Information

    Book description

    Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent account of the methods used to find all the solutions to certain diophantine equations, particularly those procedures which have been developed for use on a computer. The study is divided into three parts, the emphasis throughout being on examining approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, mainly focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers, with a basic knowledge of number theory, who are interested in solving diophantine equations using computational methods.

    Reviews

    ‘… should certainly establish itself as a key reference for established researchers and a natural starting point for new PhD students in the area.’

    E. V. Flynn Source: Bulletin of the London Mathematical Society

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