On sesquilinear forms over finite fields
Number Theory
2025-07-01 v1
Abstract
We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we calculate certain character sums to resolve enumeration problems for equations defined by sesquilinear forms. This provides a characterization of a class of maximal or minimal Artin-Schreier curves with explicit examples.
Keywords
Cite
@article{arxiv.2506.23099,
title = {On sesquilinear forms over finite fields},
author = {Ruikai Chen},
journal= {arXiv preprint arXiv:2506.23099},
year = {2025}
}