Tags » Polynomial Method

The Kakeya problem

The original Kakeya needle problem  is to  find the least amount of area required to continuously rotate a unit line segment in the (Euclidean) plane by a full rotation… 870 more words

Finite Geometry

Two proofs of the Schwartz-Zippel lemma

The fact that a univariate polynomial over a field of degree has at most zeroes is well known. It follows from the so called Factor theorem, if and only if . 799 more words

Finite Geometry

The Bombieri-Stepanov proof of the Hasse-Weil bound

Let be a finite field of order , and let be an absolutely irreducible smooth projective curve defined over (and hence over the algebraic closure of that field). 2,808 more words