It is well-known that the Apéry sequences which arise in the irrationality proofs for ζ(2) and ζ(3) satisfy many intriguing arithmetic properties and are related to the pth Fourier coefficients of modular forms. In this paper, we prove that the connection to modular forms persists for sequences associated to Brown's cellular integrals and state a general conjecture concerning supercongruences.

中文翻译：

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序列、模形式和细胞积分

众所周知，在 ζ(2) 和 ζ(3) 的非理性证明中出现的 Apéry 序列满足许多有趣的算术性质，并且与pth 模形式的傅立叶系数。在本文中，我们证明了与布朗细胞积分相关的序列与模形式的联系仍然存在，并陈述了关于超同余的一般猜想。