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math.NT2024
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…
math.NT2024
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…
math.CO2024
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…