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Selberg Sums: A New Perspective
Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in 1940s. The original versions of these sums were... -
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Amoebas, nonnegative polynomials and sums of squares supported on circuits
We completely characterize sections of the cones of nonnegative polynomials, convex polynomials and sums of squares with polynomials supported on...
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Perturbation bounds for polynomials
Using two different elementary approaches we derive a global and a local perturbation theorem on polynomial zeros that significantly improve the...
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On Location and Approximation of Clusters of Zeros: Case of Embedding Dimension One
Isolated multiple zeros or clusters of zeros of analytic maps with several variables are known to be difficult to locate and approximate. This...
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On Location and Approximation of Clusters of Zeros of Analytic Functions
At the beginning of the 1980s, M. Shub and S. Smale developed a quantitative analysis of Newton's method for multivariate analytic maps. In...