3 papers
math.NT2023
Bilinear forms with Kloosterman and Gauss sums in function fields
Christian Bagshaw
In recent years, there has been a lot of progress in obtaining non-trivial bounds for bilinear forms of Kloosterman sums in for arbitrary integers . The…
math.NT2023
Lattices in function fields and applications
Christian Bagshaw, Bryce Kerr
In recent decades, the use of ideas from Minkowski's Geometry of Numbers has gained recognition as a helpful tool in bounding the number of solutions to modular congruences with va…
math.NT2021
Energy bounds, bilinear sums and their applications in function fields
Christian Bagshaw, Igor E. Shparlinski
We obtain function field analogues of recent energy bounds on modular square roots and modular inversions and apply them to bounding some bilinear sums and to some questions regard…