Representation of Small Integers by Binary Forms

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We establish some upper bounds for the number of integer solutions to the Thue inequality |F(x, y)| ≤ m, where F is a binary form of degree n ≥ 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).

Original languageEnglish (US)
Pages (from-to)1009-1054
Number of pages46
JournalQuarterly Journal of Mathematics
Issue number4
StatePublished - Mar 5 2015

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'Representation of Small Integers by Binary Forms'. Together they form a unique fingerprint.

Cite this