Riemann problem on a two-sheeted surface of a class $O_{A^0B}$

Solvability conditions and explicit solution of the Riemann boundary value problem were derived by I. A. Bikchantaev on the case of ultrahyperelliptic surface (Riemann problem on ultrahyperelliptic surface // Russian Math. – 2000. – V. 44, № 2. – P. 17–29). The present paper generalizes the last result on the case of two-sheeted Riemann surface of the class $O_{A^0B}$.