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 ...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.展开更多
The simple continued fraction expansion of a single real number gives the best solution to its rational approximation problem. A multidimensional generalization of the simple continued fraction expanding procedure is ...The simple continued fraction expansion of a single real number gives the best solution to its rational approximation problem. A multidimensional generalization of the simple continued fraction expanding procedure is the Jacobi-Perron algorithm (JPA). This algorithm and展开更多
文摘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.
基金This work is partly supported by NSFC(No. 60173016)the National 973 Project(No.1999035804)
文摘The simple continued fraction expansion of a single real number gives the best solution to its rational approximation problem. A multidimensional generalization of the simple continued fraction expanding procedure is the Jacobi-Perron algorithm (JPA). This algorithm and
