Thue’s inequalities and the hypergeometric method

Shabnam Akhtari, N. Saradha, Divyum Sharma

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We establish upper bounds for the number of primitive integer solutions to inequalities of the shape 0 < | F(x, y) | ≤ h, where F(x, y) = (αx+ βy) r- (γx+ δy) r∈ Z[x, y] , α, β, γ and δ are algebraic constants with αδ- 0 , and r≥ 5 and h are integers. As an important application, we pay special attention to binomial Thue’s inequalities | axr- byr| ≤ c. The proofs are based on the hypergeometric method of Thue and Siegel and its refinement by Evertse.

Original languageEnglish (US)
Pages (from-to)521-567
Number of pages47
JournalRamanujan Journal
Volume45
Issue number2
DOIs
StatePublished - Feb 1 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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