Amichai Lampert

collaborators

6 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 analytic rank for trilinear forms

Amichai Lampert

In this note, we present an elementary proof of the fact that the slice rank of a trilinear form over a finite field is bounded above by a linear expression in the analytic rank. T…

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

Strength is bounded linearly by Birch rank

Benjamin Baily, Amichai Lampert

Let $f$ be a homogeneous polynomial over a field. For many fields, including number fields and function fields, we prove that the strength of $f$ is bounded above by a constant mul…

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.AG2025

Strength and partition rank under limits and field extensions

Arthur Bik, Jan Draisma, Amichai Lampert +1

The strength of a multivariate homogeneous polynomial is the minimal number of terms in an expression as a sum of products of lower-degree homogeneous polynomials. Partition rank i…