Klein Quartic Curve and its Modularity
Number Theory
2025-04-08 v1
Abstract
The local Zeta function of a variety encodes important information about the variety. From the works of Weil, Deligne, Dwork, and others, many things are known about the local Zeta function of a smooth projective variety. In this article, we find the local Zeta function for the Klein Quartic curve, , by realizing it as a quotient of degree 7 Fermat curve. We conclude by giving the associated modular forms via Galois representations.
Keywords
Cite
@article{arxiv.2504.04028,
title = {Klein Quartic Curve and its Modularity},
author = {Paresh Singh Arora},
journal= {arXiv preprint arXiv:2504.04028},
year = {2025}
}