4 papers · 1 filter
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 , with a power-saving error, whenever , the characteristic is greater than , and satisf…
Birch's theorem over function fields with quadratically many variables
Matthew Hase-Liu
For smooth hypersurfaces over rational function fields of characteristic greater than the degree and with sufficiently large constant field, we improve the number of variables requ…
A geometric approach to functional equations for general multiple Dirichlet series over function fields
Matthew Hase-Liu
Sawin recently gave an axiomatic characterization of multiple Dirichlet series over the function field and proved their existence by exhibiting the coefficients…
Efficient Point-Counting Algorithms for Superelliptic Curves
Matthew Hase-Liu, Nicholas Triantafillou
In this paper, we present efficient algorithms for computing the number of points and the order of the Jacobian group of a superelliptic curve over finite fields of prime order p.…