ARBITRARILY LONG ARITHMETIC PROGRESSIONS FOR CONTINUED FRACTIONS OF LAURENT SERIES  

作　　者：胡动刚 胡学海 

机构地区：[1]Huazhong Agricultural University

出　　处：《Acta Mathematica Scientia》2013年第4期943-949,共7页数学物理学报（B辑英文版）

基　　金：supported by NSFC(11001093,10901066)

摘　　要：A famous theorem of Szemer＇edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq（（X^-1）） be the power field of formal series with coefficients lying in Fq. In this paper, we concern with the analogous Szemeredi problem for continued fractions of Laurent series： we will show that the set of points x ∈ Fq（（X-1）） of whose sequence of degrees of partial quotients is strictly increasing and contain arbitrarily long arithmetic progressions is of Hausdorff dimension 1/2.A famous theorem of Szemer＇edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq（（X^-1）） be the power field of formal series with coefficients lying in Fq. In this paper, we concern with the analogous Szemeredi problem for continued fractions of Laurent series： we will show that the set of points x ∈ Fq（（X-1）） of whose sequence of degrees of partial quotients is strictly increasing and contain arbitrarily long arithmetic progressions is of Hausdorff dimension 1/2.

关 键 词：Szemeredi theorem continued fractions Laurent series Hausdorff dimension 

分 类 号：O173[理学—数学]