Moments on Riemann surfaces and hyperelliptic Abelian integrals
L. Gavrilov, F. Pakovich
TL;DR
This paper addresses the moment problem on Riemann surfaces and investigates conditions for the vanishing of polynomial Abelian integrals, focusing on hyperelliptic cases and their implications.
Contribution
It provides new solutions to the moment problem on Riemann surfaces and characterizes the vanishing of polynomial Abelian integrals, especially in hyperelliptic contexts.
Findings
Solved the moment problem on Riemann surfaces.
Characterized vanishing conditions for polynomial Abelian integrals.
Extended results to hyperelliptic Abelian integrals.
Abstract
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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions · Holomorphic and Operator Theory