Hypergeometric moments and Hecke trace formulas
Abstract
Abstract Moments for hypergeometric functions over finite fields were studied in the work of Ono, Pujahari, Saad, and Saikia for several 2 $$F_{1}$$ F 1 and 3 $$F_{2}$$ F 2 cases. We generalize their work to prove results for new cases where the hypergeometric data is defined over $$\mathbb {Q}$$ Q and primitive. These new moments are established using Hecke trace formulas of hypergeometric origin recently established by Hoffman, Li, Long, and Tu. We also obtain several algebraic formulas in the finite field setting and present conjectures for additional 2 $$F_{1}$$ F 1 and 3 $$F_{2}$$ F 2 moments.
Fields of Study & Subjects
Mathematical functions and polynomials
Publication details
- Journal / source
- The Ramanujan Journal
- Publisher
- Springer Science and Business Media LLC
- Volume
- 69
- Issue
- 4
- Publication date
- 1 April 2026
- Language
- EN