收稿日期: 2004-04-06
网络出版日期: 2005-01-15
基金资助
国家自然科学基金(60173016);国家973项目(1999035804)资助
Proof of the Non-Optimality of JPA and MJPA for Mult-i Formal Laurent Series
Received date: 2004-04-06
Online published: 2005-01-15
基于多重Laurent级数上的高维连分式理论，以实例证明，在对多重Laurent级数作有理逼近时，JPA及MJPA皆不能保证给出最佳有理逼近。
王全龙 , 戴宗铎 . 多重Laurent级数上的JPA与MJPA非最佳有理逼近之证[J]. 中国科学院大学学报, 2005 , 22(1) : 51 -58 . DOI: 10.7523/j.issn.2095-6134.2005.1.008
Based on the theory of multidimensional continued fraction, this paper verifies by example that neither JPA nor MJPA can guarantee opt imal rational approximation for mult-i formal Laurent series in general
[1] Hua LG. Int roduct ion to Number Theory. Beijing: Science Press, 1976(in Chinese)
[2] Bernst ein. The Jacob-i Perron algorithm, its theory and application. Lecture Note in Math. No. 207. Springer-Verlag, 1971
[3] Podsypanin, EV. A generalization of the algorithm for continued fractions related to the algorithm of Viggo Brunn. Journal of Soviet Math . , 1981,16: 885—893
[4] Schweiger F. The met rical theory of the Jacob-i Perron algorithm. Springer Lecture Notes 334. New York: Springer, 1973
[5] Brentjes AJ. Mult-i dimensional cont inued fraction algorithms.Amsterdam: Mathemat ish Centrum, 1981
[6] Meester R. A simple proof of the exponent ial convergence of the modif ied Jacob-i Perron algorithm. Erod . Th . & Dynam . Sys , 1999, 19: 1077~1083
[7] It o S , Fujii J, Higashino H, et al . On simult aneous approximat ion to(??, ??2 ) with ??3 + k??- 1= 0. J . Number Theory, 2003, 99: 255—283
[8] Lagarias JC. Best simutaneous Diophantine approximat ions . Behavior of consecut ive best approximat ions. Pacif ic Journal of Mathemati cs ,1982, 102(1) : 61—88
[9] Feng KQ, Wang FR. The Jacob-i Perron Algorithm on funct ion f ields. Algebra Coll oq. , 1994, 1: 149—158
[10] Inoue K, Nakada H.The modif ied Jacob-i Perron algorithm over F q (X ) d . Tokyo Journal of Mathematics, 2003, 26(2) : 447—470
[11] Inoue K. On the exponential convergence of Jacob-i Perron algorithm over F q (X ) d . JP Jour . Algebra, Number Theory & Appl , 2003, 3(1) : 27—41
[12] Wang QL, Wang KP, Dai ZD. On optimal simult aneous rat ional approximation to (??, ??2 )with being some kinds of cubic algebraic functions.(Preprint )
[13] Dai ZD, Wang KP , Ye DF. M- cont inued fraction expansions of mult-i Laurent series. Advances inMathematics(in China) , 2004, 33(2) : 246~248
[14] Dai ZD, Wang KP , Ye DF. Mult idimensional continued fract ion and rational approximat ion. http:????arxiv. org??abs??math. NT \ 0401141, 2004
[15] StichtenonthH. Algebraic function fields and codes. Springer-Verlag, 1991
[16] Hungerford TW. Algebra. Springer-Verlag, 1974
[17] Perron O. Grundlagen fuer eine Theorie des Jacobischen Ket tenbrunchalgorithmus. Math . Ann . , 1907, 64(1) : 1—76
[18] Weiss E. Algebraic number theory. McGraw Hill, 1963
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