On a generalization of Jacobi sums

TL;DR

This paper extends classical estimates of Jacobi sums to multi-variable multiplicative character sums over affine subspaces, providing a broader understanding of their behavior.

Contribution

It introduces a generalized estimate for multi-variable multiplicative character sums over affine subspaces, expanding the scope of classical Jacobi sum bounds.

Findings

Established a new estimate for multi-variable character sums

Unified classical Jacobi sum estimates with polynomial sums

Enhanced understanding of character sum behavior over affine spaces

Abstract

We prove an estimate for multi-variable multiplicative character sums over affine subspaces of $\mathbb A^n_k$, which generalize the well known estimates for both classical Jacobi sums and one-variable polynomial multiplicative character sums.