Periods and zeta functions for Calabi-Yau manifold

There are at least two groups of people who believe that they own the periods of CY manifolds. The first group are string theorists
who wish to compute quantities related to the compactification of string theory on these manifolds. Another group are number theorists,
since the periods encode important arithmetic information about the manifold. I will describe the periods of 1 parameter families of CY
manifolds and point out certain number theoretic features, making particular reference to the zeta functions for the manifolds.