The Ramanujan Machine project detects new expressions related to constants of interest, such as $\zeta$ function values, $\gamma$ and algebraic numbers (to name a few). In particular the project lists a number of conjectures involving even and odd $\zeta$ function values, logarithms etc. We show that many relations detected by the Ramanujan Machine Project stem from a specific algebraic observation and show how to generate infinitely many. This provides an automated proof and/or an explanation of many of the relations listed as conjectures by the project (although not all of them).
翻译:Ramanujan机器项目探测到与常数有关的新表达方式,如 $\zeta$ 函数值、 $\ gamma$ 和代数( 仅举几个例子) 。 特别是, 该项目列出了一些包含偶数和奇数 $\zeta$ 函数值、 对数等的推测。 我们显示, Ramanujan 机器项目检测到的许多关系来自特定的代数观测, 并显示如何生成无限多的关系 。 这提供了自动证明和( 或) 解释项目所列出的许多假设关系( 虽然不是全部) 。