Klein Quartic Curve and its Modularity
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=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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