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arXiv · 1406.5523

Experiments on the zeros of harmonic polynomials using certified counting

Jonathan D. Hauenstein·Antonio Lerario·Erik Lundberg·Dhagash Mehta
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Abstract

Motivated by Wilmshurst's conjecture, we investigate the zeros of harmonic polynomials. We utilize a certified counting approach which is a combination of two methods from numerical algebraic geometry: numerical polynomial homotopy continuation to compute a numerical approximation of each zero and Smale's alpha-theory to certify the results. Using this approach, we provide new examples of harmonic polynomials having the most extreme number of zeros known so far; we also study the mean and variance of the number of zeros of random harmonic polynomials.

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Jonathan D. Hauenstein, Antonio Lerario, Erik Lundberg, Dhagash Mehta. 2014-06-20. Experiments on the zeros of harmonic polynomials using certified counting. https://arxiv.org/abs/1406.5523

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