On optimal simultaneous rational approximation to with being some kind of cubic algebraic function |
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| Authors: | Quanlong Wang Kunpeng Wang Zongduo Dai |
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| Institution: | aSchool of Mathematical Sciences, Peking University, Beijing 100871, PR China;bState Key Laboratory of Information Security (Graduate School of Chinese Academy of Sciences), Beijing 100049, PR China |
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| Abstract: | It is shown that each rational approximant to (ω,ω2)τ given by the Jacobi–Perron algorithm (JPA) or modified Jacobi–Perron algorithm (MJPA) is optimal, where ω is an algebraic function (a formal Laurent series over a finite field) satisfying ω3+kω-1=0 or ω3+kdω-d=0. A result similar to the main result of Ito et al. On simultaneous approximation to (α,α2) with α3+kα-1=0, J. Number Theory 99 (2003) 255–283] is obtained. |
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| Keywords: | Multi-dimensional continued fraction algorithm Jacobi– Perron algorithm Modified Jacobi– Perron algorithm Optimal simultaneous rational approximation |
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