论文标题
自动发现新$ l $ - 功能关系
Automated Discovery of New $L$-Function Relations
论文作者
论文摘要
$ l $ - 功能通常编码有关数学对象的有趣信息。本文报告了迄今为止文献中从未出现过的这种功能之间的29个身份。其中有9个完整的证明；所有其他人都经过了广泛的数值检查，我们欢迎证明其（在）有效性的证据。 我们为获得这些身份的方法设计的方法是一个两步过程，从而自动生成，获得，测试并最终正式证明了候选身份的列表。但是，该方法仅是自动化的\ emph {semi-}，因为人类干预对于后处理阶段是必要的，以确定猜想身份的最通用形式并为其提供证明。 这项工作补充了文献中的其他实例，在文献中，自动化符号计算已成为朝着定理证明的富有成效的一步，并且可以进一步扩展到多个方向，以探索$ l $ dunctions和类似结构的代数景观。
$L$-functions typically encode interesting information about mathematical objects. This paper reports 29 identities between such functions that hitherto never appeared in the literature. Of these we have a complete proof for 9; all others are extensively numerically checked and we welcome proofs of their (in)validity. The method we devised to obtain these identities is a two-step process whereby a list of candidate identities is automatically generated, obtained, tested, and ultimately formally proven. The approach is however only \emph{semi-}automated as human intervention is necessary for the post-processing phase, to determine the most general form of a conjectured identity and to provide a proof for them. This work complements other instances in the literature where automated symbolic computation has served as a productive step toward theorem proving and can be extended in several directions further to explore the algebraic landscape of $L$-functions and similar constructions.
