The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contains applications to algebraic integers and units, the Mandelbrot set, elliptic curves, Fermat curves, and modular curves. A long chapter is devoted to examples, including methods for computing capacities.

Another chapter contains extensions of the theorem, including variants on Berkovich curves.

### Capacity Theory with Local Rationality: The Strong Fekete-Szego Theorem on Curves

The proof uses both algebraic and analytic methods, and draws on arithmetic and algebraic geometry, potential theory, and approximation theory. It introduces new ideas and tools which may be useful in other settings, including the local action of the Jacobian on a curve, the ''universal function'' of given degree on a curve, the theory of inner capacities and Green's functions, and the construction of near-extremal approximating functions by means of the canonical distance.

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USD Sign in to Purchase Instantly. Overview This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szego theorem with local rationality conditions. Product Details. Average Review.

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## Rumely, Robert 1952-

The authors develop a theory for the existence of perfect matchings in hypergraphs under quite The authors develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: 'space barriers' from convex geometry, and 'divisibility barriers' View Product.

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This volume contains the proceedings of the Clifford Lectures on Algebraic Groups: Structures and This volume consists of six articles on algebraic groups, including an enhanced exposition Axiomatic geometry American Mathematical Society, Pure and applied undergraduate texts ; Memoires de la Societe mathematique de France ; nouvelle serie ; no.

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