5 papers
Bilinear Kloosterman sums in function fields and the distribution of irreducible polynomials
Christian Bagshaw
Inspired by the work of Bourgain and Garaev (2013), we provide new bounds for certain weighted bilinear Kloosterman sums in polynomial rings over a finite field. As an application,…
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…
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…
Square-free smooth polynomials in residue classes and generators of irreducible polynomials
Christian Bagshaw
Building upon the work of A. Booker and C. Pomerance (2017), we prove that for a prime power , every residue class modulo an irreducible polynomial $F \in \mathbb{F}_q[X]…
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…