  We study one-parameter deformations of Calabi-Yau type Fermat polynomial
singularities along degree-one directions. We show that twisted sectors in the
vanishing cohomology are components of automorphic forms for certain triangular
groups. We prove consequentially that genus zero Gromov-Witten generating
series of the corresponding Fermat Calabi-Yau varieties are components of
automorphic forms. The main tools we use are mixed Hodge structures for
quasi-homogeneous polynomial singularities, Riemann-Hilbert correspondence, and
genus zero mirror symmetry.
