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arXiv · 2504.04028

Klein Quartic Curve and its Modularity

Paresh Singh Arora
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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, $x^3y+y^3z+z^3x=0$, by realizing it as a quotient of degree 7 Fermat curve. We conclude by giving the associated modular forms via Galois representations.

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Paresh Singh Arora. 2025-04-05. Klein Quartic Curve and its Modularity. https://arxiv.org/abs/2504.04028

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