论文标题
D限制，合理性和高度II：一组正密度的下限
D-finiteness, rationality, and height II: lower bounds over a set of positive density
论文作者
论文摘要
我们考虑d-finite Power系列$ f（z）= \ sum a_n z^n $，带有数字字段$ k $的系数。我们表明，有一个二分法，该二分法是$ h（a_n）$作为$ n $的行为，其中$ h $是绝对的对数Weil高度。作为我们结果的直接结果，我们有$ f（z）$是理性的，或$ h（a_n）> [k：\ mathbb {q}]^{ - 1} \ cdot \ cdot \ cdot \ log（n）+o（n）+o（1）$ for $ n $ for $ n $ for $ n $在$ k = k = k = \ mathbbbbbbbbbbbbbbbbbbbbbbb = pasten pastion中最好。
We consider D-finite power series $f(z)=\sum a_n z^n$ with coefficients in a number field $K$. We show that there is a dichotomy governing the behaviour of $h(a_n)$ as a function of $n$, where $h$ is the absolute logarithmic Weil height. As an immediate consequence of our results, we have that either $f(z)$ is rational or $h(a_n)>[K:\mathbb{Q}]^{-1}\cdot \log(n)+O(1)$ for $n$ in a set of positive upper density and this is best possible when $K=\mathbb{Q}$.
