Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Mathematics
Reduction Of L-Functions Of Elliptic Curves Modulo Integers, Félix Baril Boudreau
Reduction Of L-Functions Of Elliptic Curves Modulo Integers, Félix Baril Boudreau
Electronic Thesis and Dissertation Repository
Let $\mathbb{F}_q$ be a finite field of size $q$, where $q$ is a power of a prime $p \geq 5$. Let $C$ be a smooth, proper, and geometrically connected curve over $\mathbb{F}_q$. Consider an elliptic curve $E$ over the function field $K$ of $C$ with nonconstant $j$-invariant. One can attach to $E$ its $L$-function $L(T,E/K)$, which is a generating function that contains information about the reduction types of $E$ at the different places of $K$. The $L$-function of $E/K$ was proven to be a polynomial in $\mathbb{Z}[T]$.
In 1985, Schoof devised an algorithm to compute the zeta function of an …