A Panorama in Number Theory or The View from Baker's Garden: Modular Forms, Elliptic Curves and the ABC -Conjecture

  title={A Panorama in Number Theory or The View from Baker's Garden: Modular Forms, Elliptic Curves and the ABC -Conjecture},
  author={Dorian Goldfeld},
The ABC–conjecture was first formulated by David Masser and Joseph Osterlé (see [Ost]) in 1985. Curiously, although this conjecture could have been formulated in the last century, its discovery was based on modern research in the theory of function fields and elliptic curves, which suggests that it is a statement about ramification in arithmetic algebraic geometry. The ABC–conjecture seems connected with many diverse and well known problems in number theory and always seems to lie on the… 

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