Publication Date:
2015-12-09
Description:
We establish some upper bounds for the number of integer solutions to the Thue inequality $|F(x , y)| \leq m$ , where $F$ is a binary form of degree $n \geq 3$ and with non-zero discriminant $D$ , and $m$ is an integer. Our upper bounds are independent of $m$ , when $m$ is smaller than $|D|^{{1}/{4(n-1)}}$ . We also consider the Thue equation $|F(x , y)| = m$ and give some upper bounds for the number of its integral solutions. In the case of equation, our upper bounds will be independent of integer $m$ , when $m 〈 |D|^{{1}/{2(n-1)}}$ .
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
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