Quartic power series in $_3((T^{-1}))$ with bounded partial quotients
Quartic power series in $_3((T^{-1}))$ with bounded partial quotients
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DOI：
10.4064/aa-95-1-49-59
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发表时间：
2000
期刊：
影响因子：
0.7
通讯作者：
A. Lasjaunias
中科院分区：
文献类型：
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作者：
A. Lasjaunias
本文讨论函数域上的丢番图逼近和连分式。在经典理论中，Z、Q和R的作用分别由K[T ]、K（T）和K（（T））起，其中K是任意给定的域。幂级数域K（（T））的一个元素将表示为α = akT k +ak− 1 T k−1 +..其中k ∈ Z，ai ∈ K且ak 6= 0。有理数k称为α的度数，记为deg α。超度量绝对值定义为：|α| = |不|α和|0| = 0，其中|不|是大于1的固定真实的数。因此，域K（（T））应该被看作是域K（T）对于这个绝对值的完备化。
We are concerned with diophantine approximation and continued fractions in function fields. The rôles of Z, Q, and R in the classical theory are played by K[T ], K(T ) and K((T)), where K is an arbitrary given field. An element of the field K((T)) of power series will be denoted by α = akT k +ak−1T k−1 + .... where k ∈ Z, ai ∈ K and ak 6= 0. The rational k is called the degree of α, denoted by deg α. An ultrametric absolute value is defined by |α| = |T | α and |0| = 0, where |T | is a fixed real number greater than 1. Thus the field K((T)) should be viewed as a completion of the field K(T ) for this absolute value.