On approximation in the mean on curves in the complex plane by polynomials with integer coefficients

This work investigates conditions fot the possibility of approximating functions $f(z)$ in the $p$ th order mean on a curve $C$ with arbitrary accuracy by polynomials whose coefficients are algebraic integers from a complex quadratic field. The case when $f(z)$ is an analytic function of class $E_p$ in the region bounded by a closed curve $C$ i s examined, as is the case when $f(z)$ is integrable of degree $p$ on a curve $C$ which is not closed.