On the moments of exponential sums over r‐free polynomials
Abstract
Abstract Let denote the ring of polynomials over the finite field . Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of th moments of exponential sums over ‐free polynomials in for all . In the supercritical case , we acquire an asymptotic formula using a function field analog of the Hardy–Littlewood circle method.
Fields of Study & Subjects
Mathematical functions and polynomials
Analytic Number Theory Research
Mathematics and Applications
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN