Mirror symmetric Gamma conjecture for Fano and Calabi-Yau manifolds

The mirror symmetric Gamma conjecture roughly speaking says that the Gamma class of a manifold determines the asymptotics of (exponential) periods of the mirror. We recast the method in [Iri11] in a more general context and show that the mirror symmetric Gamma conjecture for a Fano manifold F implies, via Laplace transformation, that for the total space K_F of the canonical bundle or for anticanonical sections in F. More generally, we discuss the mirror symmetric Gamma conjecture for the total space of a sum of anti-nef line bundles over F or for nef complete intersections in F.