2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59088We show that counting functions of covers of $\mathbb{C}^\times$ are equal to sums of integrals associated to certain `Feynman' graphs. This is an analogue of the mirror symmetry for elliptic curves by Dijkgraaf.8 pages, 3 figures, AMS-LaTeX, to appear in Proc. Amer. Math. SocAlgebraic GeometryCombinatorics14N10 (Primary) 05A15, 20B30 (Secondary)text