Amichai Lampert

most citedBias implies low rank for quartic polynomials

5 citations · 5 across the 3 of their papers we have counts for

collaborators

4 papers

math.NT2025

Polynomial Bounds for Birch's Theorem

Amichai Lampert, Andrew Snowden, Tamar Ziegler

Let $K$ be a number field and $f_{1}, \dots, f_{s} \in K [x_{1}, \dots, x_{n}]$ forms of odd degrees. In 1957, Birch proved that if $n$ is sufficiently large then the forms always have a nontr…

math.CO2025

Slice rank and partition rank of the determinant

Amichai Lampert, Guy Moshkovitz

The Laplace expansion expresses the $n \times n$ determinant $det_{n}$ as a sum of $n$ products. Do shorter expansions exist? In this paper we: - Fully determine the slice rank deco…

math.NT2025

Density of solutions for systems of forms

Amichai Lampert

Let $K$ be a field of characteristic zero over which every diagonal form in sufficiently many variables admits a nontrivial solution. For example, $K$ may be a totally imaginary nu…

math.CO2019★ 5 cited

Bias implies low rank for quartic polynomials

Amichai Lampert

We investigate the structure of polynomials of degree four in many variables over a fixed prime field $F = F_{p}$ . In 2007, Green and Tao proved that if a polynomia…