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 language | English (US) |
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Pages (from-to) | 1377-1382 |
Number of pages | 6 |
Journal | Rocky Mountain Journal of Mathematics |
Volume | 44 |
Issue number | 4 |
DOIs | |
State | Published - 2014 |
All Science Journal Classification (ASJC) codes
- General Mathematics