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Zeta functions are typically analogues or generalizations of the Riemann zeta function. Examples include Dedekind zeta functions of number fields, and zeta functions of varieties over finite fields. They are typically initially defined as formal generating functions, but often admit analytic continuations.
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What are positive divisors of degree 2 on Elliptic Curve $y^2=x^3-x-1$ over $\mathbb{F}_3$?
For a nonsingular cubic curve $X \subset \mathbb{P}^2$ over a finite field $\mathbb{F}_q$, if $a_1$ is the number of $\mathbb{F}_q$-points of $X$, and $a_2$ is the number of effective degree two divis …