Integer points on elliptic curves

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Abstract

We show that the number of integer points on an elliptic curve y2 = f(x) with X0 < x ≤ X0 + X is 蠐 X1/2 where the implicit constant depends at most on the degree of f(x). This improves on various bounds of Cohen [4], Bombieri and Pila [1] and of Pila [9], and others. In particular it follows that the number of positive integral solutions to x3 + y2 = n is 蠐 n1/6.

Original languageEnglish (US)
Pages (from-to)1377-1382
Number of pages6
JournalRocky Mountain Journal of Mathematics
Volume44
Issue number4
DOIs
Publication statusPublished - Jan 1 2014

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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