English

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, x3y+y3z+z3x=0x^3y+y^3z+z^3x=0, 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}
}
R2 v1 2026-06-28T22:47:53.870Z