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We use localization techniques to study the non-perturbative properties of anN=2 superconformal gauge theory with gauge group SU(3) and six fundamentalflavours. The instanton corrections to the prepotential, the dual periods andthe period matrix are calculated in a locus of special vacua possessing a Z_3symmetry. In a semi-classical expansion, we show that these observables areconstrained by S-duality via a modular anomaly equation which takes the form ofa recursion relation. The solutions of the recursion relation are quasi-modularfunctions of Gamma_1(3), which is a subgroup of the S-duality group and is alsoa congruence subgroup of SL(2,Z).

Modular anomaly equations and S-duality in N=2 conformal SQCD