Burgess‐type character sum estimates over generalized arithmetic progressions of rank 2
Abstract
Abstract We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank 2 in prime fields . The core of our proof is a sharp upper bound for the multiplicative energy of these sets, established by adapting an argument of Konyagin and leveraging tools from the geometry of numbers. A key step in our argument involves establishing new upper bounds for the sizes of Bohr sets, which may be of independent interest.
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN