A Survey of Diophantine Approximationin Fields of Power Series
A Survey of Diophantine Approximationin Fields of Power Series
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DOI：
10.1007/s006050070036
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发表时间：
2000-08
期刊：
影响因子：
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通讯作者：
A. Lasjaunias
中科院分区：
文献类型：
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作者：
A. Lasjaunias
幂级数域（或者更好地称为形式数）是真实的数域的类似物。数论中的许多问题都是在真实的数的背景下研究的，这些问题可以转置到幂级数的背景下来研究。代数真实的数的有理逼近的研究从世纪中期Liouville的工作到1955年Roth的著名定理的建立，得到了很大的发展。近三十年来，许多数学家研究了幂级数域上的丢番图逼近。我们在这里提出一个关于这个问题的现有知识的总结，强调与真实的数情况的类比和区别。
The fields of power series (or perhaps better called formal numbers) are analogues of the field of real numbers. Many questions in number theory which have been studied in the setting of the real numbers can be transposed to the setting of the power series. The study of rational approximation to algebraic real numbers has been intensively developped starting from the middle of the nineteenth century with the work of Liouville up to the celebrated theorem of Roth established in 1955. In the last thirty years, several mathematicians have studied diophantine approximation in fields of power series. We present here a summary of the present knowledge on this subject, emphasizing the analogies and differences with the situation in the real numbers case.