Andrew Snowden

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.NT2024

Two improvements in Birch's theorem on forms

Amichai Lampert, Andrew Snowden

Let $K$ 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, $K$ could be the fiel…

math.AG2024

The geometry of polynomial representations in positive characteristic

Arthur Bik, Jan Draisma, Andrew Snowden

A $GL$ -variety is a (typically infinite dimensional) variety modeled on the polynomial representation theory of the general linear group. In previous work, we studied thes…

math.NT2024

Two improvements in Brauer's theorem on forms

Arthur Bik, Jan Draisma, Andrew Snowden

Let $k$ be a Brauer field, that is, a field over which every diagonal form in sufficiently many variables has a nonzero solution; for instance, $k$ could be an imaginary quadratic…