Abstract
LetR be the Riemann surface of the functionu(z) specified by the equationun=P(z) withn e ℕ,n ≥ 2, andz e ℂ, whereP(z) is an entire function with infinitely many simple zeros. OnR, the Riemann boundary-value problem for an arbitrary piecewise smooth contour Γ is considered. Necessary and sufficient conditions for its solvability are obtained, and its explicit solution is constructed.
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