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  3. Elliptic Curves
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  • Publisher:
    Cambridge University Press
    Publication date:
    February 2025
    March 2025
    ISBN:
    9781009602129
    9781009602112
    DOI:
    https://doi.org/10.1017/9781009602129
    Dimensions:
    Weight & Pages:
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.47kg, 314 Pages
    • Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    Cambridge Mathematical Library
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    Cambridge Mathematical Library
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    Book description

    The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This book, reissued with a new Foreword, presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.

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