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

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  • Tymoteusz Chmiel
  • Sławomir Cynk

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.

Suggested Citation

  • Tymoteusz Chmiel & Sławomir Cynk, 2023. "Periods of singular double octic Calabi–Yau threefolds and modular forms," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3257-3271, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3257-3271
    DOI: 10.1002/mana.202200085
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