Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4663762 | Acta Mathematica Scientia | 2013 | 7 Pages |
Abstract
A famous theorem of Szemer'edi asserts that any subset of integers with positive upper density contains arbitrarily arithmetic progressions. Let q be a finite field with q elements and q((X−1)) be the power field of formal series with coefficients lying in q. In this paper, we concern with the analogous Szemerédi problem for continued fractions of Laurent series: we will show that the set of points x ∈ q((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.
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Mathematics
Mathematics (General)