LAUSR

DOI: https://doi.org/10.1090/noti2073 elementary and intuitive way to estimate or compute the pdivisibility of exponential sums, which is particularly convenient in the applications. The covering method allows us to determine solvability of systems of polynomial equations, improve the search for balanced Boolean functions, give better estimates for covering radius of codes, and has many other applications. Solvability of systems of polynomial equations. One of the prominent problems in mathematics is to determine if a polynomial equation has solutions. In 1935 Artin conjectured that a homogeneous polynomial over a finite field has a nontrivial zero if the number of variables is larger than the degree. Chevalley obtained almost immediately a slightly better result changing the hypothesis of