A simply connected surface of general type with p_g=0 and K²=3

Motivated by a recent result of Y. Lee and the second author[7], we construct a simply connected minimal complex surface of general type with p_g=0 and K^2=3 using a rational blow-down surgery and Q-Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic 4-manifold with b_2^+=1 and K^2=4.