Hausdorff measure of zeros of polynomials

2023/12/29 by Andrew Murdza, Murdza, Andrew, Khai T. Nguyen +3
Mathematics · #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2312.17462

openalex publication_date 2023/12/29 · openalex created_date 2024/01/02 · openalex updated_date 2026/07/28

Abstract

The paper provides an elementary proof establishing a sharp universal bound on the (d-1)-Hausdorff measure of the zeros of any nontrivial multivariable polynomial p:ℝ^d→ℝ within a d-dimensional cube of size r. This bound depends solely on the parameter r, the dimension d, and the degrees of p.

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