A Course in p-adic Analysis
A Course in p-adic Analysis
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DOI：
10.1007/978-1-4757-3254-2
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发表时间：
2000-05
期刊：
影响因子：
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通讯作者：
A. Robert
中科院分区：
文献类型：
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作者：
A. Robert
Kurt Hensel（1861-1941）在世纪之交发现了p-adic数。这些奇特的数字（或者说它们最初是这样出现的）现在在数学界已经得到了很好的认可，也越来越多地被物理学家使用。这本书提供了一个独立的介绍基本p-adic分析。作者对这一领域的分析主题特别感兴趣。一些功能没有处理在其他介绍p-adic分析文本是拓扑模型的p-adic空间内欧几里德空间，建设球面完全领域，一个p-adic中值定理和一些后果，一个特殊情况下Hazewinkel的功能方程引理，剩余公式的马勒扩展，最重要的是治疗的分析元素。
Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.