Periods of singular double octic Calabi–Yau threefolds and modular forms

Tymoteusz Chmiel and Sławomir Cynk

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3257-3271

Abstract: By the modularity theorem, every rigid Calabi–Yau threefold X has associated modular form f such that the equality of L‐functions L(X,s)=L(f,s)$L(X,s)=L(f,s)$ holds. In this case, period integrals of X are expected to be expressible in terms of the special values L(f,1)$L(f,1)$ and L(f,2)$L(f,2)$. We propose a similar interpretation of period integrals of a nodal model of X. It is given in terms of certain variants of a Mellin transform of f. We provide numerical evidence toward this interpretation based on a case of double octics.

Date: 2023
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