Glasnik Matematicki, Vol. 53, No. 2 (2018), 229-238.

TOTALLY REAL THUE INEQUALITIES OVER IMAGINARY QUADRATIC FIELDS

István Gaál, Borka Jadrijević and László Remete

University of Debrecen, Mathematical Institute, H-4002 Debrecen Pf.400., Hungary
e-mail: gaal.istvan@unideb.hu

University of Split, Faculty of Science, Rudjera Boškovića 33, 21000 Split, Croatia
e-mail: borka@pmfst.hr

University of Debrecen, Mathematical Institute, H-4002 Debrecen Pf.400., Hungary
e-mail: remete.laszlo@science.unideb.hu

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.

2010 Mathematics Subject Classification.   11D59, 11D57

Key words and phrases.   Relative Thue equations, Thue inequalities

Full text (PDF) (free access)

DOI: 10.3336/gm.53.2.02

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