Moments on Riemann surfaces and hyperelliptic Abelian integrals
  In the present paper we solve the following different but interrelated problems: (a) the moment problem on Riemann surfaces, (b) the vanishing problem of polynomial Abelian integrals of dimension zero on the projective plane, (c) the vanishing problem of polynomial hyperelliptic Abelian integrals. 
L. Gavrilov, F. Pakovich
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