Mirror symmetry and C^\times

Abstract

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