Extremal polynomials on arcs of the circle with zeros on these arcs

The paper gives a solution of an extremal problem of finding monic polynomial least deviating from zero on several arcs of the unit circle, under some restrictions on the location of zeros and additional conditions on mutual position of the arcs. The extremal polynomial is represented in the terms of density of harmonic measure. The work is done under the financial support of RFFI (Project 07-01-00167) and the President of RF Grant (Project NSh-2970.2008.1).