论文标题
Agafonov的Agafonov定理证明：现代帐户和新见解
Agafonov's Proof of Agafonov's Theorem: A Modern Account and New Insights
论文作者
论文摘要
我们对Agafonov的同名定理的原始证明进行了现代描述。最初的证据仅在俄罗斯的日记中报道，而西方文学中最常见的作品是英文翻译的摘要版本的英文翻译，其中包含证据，主要证明在很大程度上依赖于当天俄罗斯数学圈子中所知的材料，这些材料可能掩盖了对现代读者的主要论证，而不是在现代账户中占有原始的证明。为了清晰的利益，对阿加富诺夫的原始论点进行了修饰。我们认为，现代账户为定理的基本现象提供了新的见解。我们还为阿加福诺夫的工作提供了一些历史背景，包括对导致阿加福诺夫自己证明的一些想法的简短描述，尤其是强调了后尼科娃的重要工作。
We give a modern account of Agafonov's original proof of his eponymous theorem. The original proof was only reported in Russian in a journal not widely available, and the work most commonly cited in western literature is instead the English translation of a summary version containing no proofs, and the main proof relied heavily on material well-known in Russian mathematical circles of the day, which perhaps obscures the main thrust of argumentation for modern readers.Our present account recasts Aganofov's arguments using more basic building blocks than in the original proof, and contains some further embellishments to Agafonov's original arguments, made in the interest of clarity. We posit that the modern account provides new insight to the underlying phenomena of the theorem.We also provides some historical context to Agafonov's work, including a short description of some of the ideas that led to Agafonov's own proof, especially emphasizing the important work of Postnikova.
