Original scientific paper

https://doi.org/10.3336/gm.53.2.02

Totally real Thue inequalities over imaginary quadratic fields

István Gaál ; University of Debrecen, Mathematical Institute, H-4002 Debrecen Pf.400., Hungary
Borka Jadrijević orcid.org/0000-0002-5913-3719 ; University of Split, Faculty of Science, Rudjera Boškovića 33, 21000 Split, Croatia
László Remete ; University of Debrecen, Mathematical Institute, H-4002 Debrecen Pf.400., Hungary

Abstract

Let F(x,y) be an irreducible binary form of degree ≥ 3 with integer coefficients and with real roots. Let M be an imaginary quadratic field with ring of integers ℤM. Let K>0. We describe an efficient method how to reduce the resolution of the relative Thue inequalities
|F(x,y)|≤ K (x,y ℤM)
to the resolution of absolute Thue inequalities of type
|F(x,y)|≤ k (x,y ℤ).
We illustrate our method with an explicit example.

Keywords

Relative Thue equations; Thue inequalities

Hrčak ID:

214473

URI

https://hrcak.srce.hr/214473

Publication date:

30.12.2018.

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