Frobenius structure and p-adic zeta values

Abstract

For differential operators of Calabi-Yau type, Candelas, De la Ossa and van Straten conjecture the appearance of p-adic zeta values in the matrix entries of their p-adic Frobenius structure expressed in the standard basis of solutions near a point of maximal unipotent local monodromy. We prove that this phenomenon holds for simplicial and hyperoctahedral families of Calabi-Yau hypersurfaces in n dimensions, in which case the limits of the Frobenius matrix entries are rational linear combinations of products of ζp(k) with 1<k<n.