Geodesic
On approximation in the mean on curves in the complex plane by
Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 551-567.

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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. 
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S. Ya. Al'per; I. Yu. Vinogradova. On approximation in the mean on curves in the complex plane by. Izvestiya. Mathematics , Tome 4 (1970) no. 3, pp. 551-567. http://geodesic.mathdoc.fr/item/IM2_1970_4_3_a5/

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