  We propose a new method to compute asymptotics of periods using tropical
geometry, in which the Riemann zeta values appear naturally as error terms in
tropicalization. Our method suggests how the Gamma class should arise from the
Strominger-Yau-Zaslow conjecture. We use it to give a new proof of (a version
of) the Gamma Conjecture for Batyrev pairs of mirror Calabi-Yau hypersurfaces.
