The number of solutions to cubic
نویسنده
چکیده
is also finite, since obviously such a form takes integral values at integral points. Let NF (m) denote the number of integral solutions to the Thue inequality above and consider the region RF = {(x, y) ∈ R2 : |F (x, y)| ≤ 1}. Then the dilation of RF by m1/d consists of all (x, y) ∈ R2 with |F (x, y)| ≤ m, so that one would expect mAF , where AF is the area of RF , to approximate NF (m). Indeed, Mahler [M1] showed that |NF (m)−mAF | = O(m1/(d−1)) ,
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