Mirror symmetry and C^\times

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We 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. Soc

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