论文标题
加法引起的裂差：模块化函数应用于无限分区一致性家族
Divisibility Arising From Addition: The Application of Modular Functions to Infinite Partition Congruence Families
论文作者
论文摘要
现在，一个多世纪以来，分区一致性的理论一直是一个令人着迷且困难的主题。在尝试证明给定的一致性家族时，多种可能的并发症包括基础模块化曲线的属，模块化函数相关序列的表示困难以及有关分段$ \ ell $ $ $ - $ - ad-aadic融合的困难。但是，我们对该主题的了解已经大大发展，并继续发展。在这项非常简短的调查中，我们将讨论模块化功能在证明分区一致性（理论和计算）中的实用性，以及尚未克服的主题中的许多问题。
The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve, representation difficulties of the associated sequences of modular functions, and difficulties regarding the piecewise $\ell$-adic convergence of elements of the associated space of modular functions. However, our knowledge of the subject has developed substantially and continues to develop. In this very brief survey, we will discuss the utility of modular functions in proving partition congruences, both theoretical and computational, and many of the problems in the subject that are yet to be overcome.
