On optimal simultaneous rational approximation to (W,W2)t with ? being some kind of cubic algebraic function

• Autores: Quanlong Wang, Kunpeng Wang, Zongduo Dai
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 148, Nº 2, 2007, págs. 194-210
• Idioma: inglés
• DOI: 10.1016/j.jat.2007.04.002
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• Resumen

  • It is shown that each rational approximant to (?,?2)t given by the Jacobi¿Perron algorithm (JPA) or modified Jacobi¿Perron algorithm (MJPA) is optimal, where ? is an algebraic function (a formal Laurent series over a finite field) satisfying ?3+k?-1=0 or ?3+kd?-d=0. A result similar to the main result of Ito et al. [On simultaneous approximation to (a,a2) with a3+ka-1=0, J. Number Theory 99 (2003) 255¿283] is obtained.