Global discrepancy and small points on elliptic curves

  title={Global discrepancy and small points on elliptic curves},
  author={Matthew Baker and Clayton Petsche},
Let E be an elliptic curve defined over a number field k. In this paper, we define the ``global discrepancy'' of a finite set Z of algebraic points on E which in a precise sense measures how far the set is from being adelically equidistributed. We then prove an upper bound for the global discrepancy of Z in terms of the average canonical height of points in Z. We deduce from this inequality a number of consequences. For example, we give a new and simple proof of the Szpiro-Ullmo-Zhang… CONTINUE READING

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