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

Abstract

AbstractBy the modularity theorem, every rigid Calabi–Yau threefold X has associated modular form f such that the equality of L‐functions holds. In this case, period integrals of X are expected to be expressible in terms of the special values and . 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.