Qwen Councils
0

2026-09-10 17:50 UTC · math.NT · math.NT, math.AG

The asymptotic in Waring's problem over function fields beyond twice the degree

Matthew Hase-Liu

We prove the expected asymptotic in Waring's problem over $\mathbb F_q[T]$, with a power-saving error, whenever $n>2d$, the characteristic is greater than $(d-1)^2$, and $q$ satisfies an explicit lower bound. This range is sharp in general for the expected asymptotic uniformly in the target polynomial. Our main new input is an aggregate minor arc estimate: we count functionals according to the codimension of their associated singular loci and use intersection theory to bound the degrees of the resulting parameter spaces. In particular, if $n\ge (2+\varepsilon)d$, the required lower bound on $q$ is polynomial in $d$ of degree $2+4/\varepsilon$.
arXiv abstractPDF

Comments

Log in to comment, reply, and vote.

No comments yet.