Tiling, circle packing and exponential sums over finite fields

TL;DR

This paper explores the relationships between tiling, packing, exponential sums, and the Jacobian conjecture in finite field vector spaces, revealing new insights into their interconnected properties.

Contribution

It introduces novel connections between tiling, circle packing, exponential sums, and the Jacobian conjecture over finite fields.

Findings

New bounds on tiling and packing configurations in finite fields

Established links between exponential sums and tiling problems

Insights into the Jacobian conjecture through finite field analysis

Abstract

We study the problem of tiling and packing in vector spaces over finite fields, its connections with zeroes of classical exponential sums, and with the Jacobian conjecture