Capacity Theory With Local Rationality: The Strong Fekete-Szego Theorem on Curves (Mathematical Surveys and Monographs, 193, Band 193) - Hardcover

Inhaltsangabe

Rumely's introduction to this exposition on the Fekete-Szegö theorem includes a sketch of the basic proof and contextualizes its development with the Robinson theorem on totally real algebraic integers in an interval and Cantor's extension with splitting conditions. The first chapter lays out several variants of the theorem, and the second illustrates with examples on elliptic, Fermat, and modular curves. Systematic development of the theory begins with notation and conventions, summaries of capacities and Green's functions, and continues with reduction of the variants back to the original theorem with local rationality conditions. Initial approximating functions are treated for the Archimedean and non-Archimedean cases. The last suite of chapters cover the global patching construction, followed by local patching for varying conditions. Appendices present additional proofs on related topics including potential theory, oscillating pseudopolynomials, the universal function, and local action of the Jacobian. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

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