5 citations · 10 across the 11 of their papers we have counts for
13 papers
Polynomial Bounds for Birch's Theorem
Amichai Lampert, Andrew Snowden, Tamar Ziegler
Let be a number field and forms of odd degrees. In 1957, Birch proved that if is sufficiently large then the forms always have a nontr…
Slice rank and partition rank of the determinant
Amichai Lampert, Guy Moshkovitz
The Laplace expansion expresses the determinant as a sum of products. Do shorter expansions exist? In this paper we: - Fully determine the slice rank deco…
Density of solutions for systems of forms
Amichai Lampert
Let be a field of characteristic zero over which every diagonal form in sufficiently many variables admits a nontrivial solution. For example, may be a totally imaginary nu…
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…
Strength is bounded linearly by Birch rank
Benjamin Baily, Amichai Lampert
Let be a homogeneous polynomial over a field. For many fields, including number fields and function fields, we prove that the strength of is bounded above by a constant mul…
Two improvements in Birch's theorem on forms
Amichai Lampert, Andrew Snowden
Let be a Birch field, that is, a field for which every diagonal form of odd degree in sufficiently many variables admits a non-zero solution; for example, could be the fiel…
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…
Small ideals in polynomial rings and applications
Amichai Lampert
Let be a field which is either finite or algebraically closed and let We prove that any homogeneous of positive…
On rank in algebraic closure
Amichai Lampert, Tamar Ziegler
Let be a field and a form (homogeneous polynomial) of degree The -Schmidt rank of i…
Relative Rank and Regularization
Amichai Lampert, Tamar Ziegler
We introduce a new concept of rank - relative rank associated to a filtered collection of polynomials. When the filtration is trivial our relative rank coincides with Schmidt rank…
Schmidt rank and singularities
David Kazhdan, Amichai Lampert, Alexander Polishchuk
We revisit Schmidt's theorem connecting the Schmidt rank of a tensor with the codimension of a certain variety and adapt the proof to the case of arbitrary characteristic. We also…
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 . In 2007, Green and Tao proved that if a polynomia…
On Maximizing the Speed of a Random Walk in Fixed Environments
Amichai Lampert, Assaf Shapira
We consider a random walk in a fixed Z environment composed of two point types: (q,1-q) and (p,1-p) for 1/2<q<p. We study the expected hitting time at N for a given number k of p-d…