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SUMMARY:Felix Baril Boudreau (Western Univ.)
DTSTART:20211102T210000Z
DTEND:20211102T220000Z
DTSTAMP:20260423T010139Z
UID:UAANTS/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/27/">
 Computing an L-function modulo a prime</a>\nby Felix Baril Boudreau (Weste
 rn Univ.) as part of University of Arizona Algebra and Number Theory Semin
 ar\n\n\nAbstract\nLet $E$ be an elliptic curve with non-constant $j$-invar
 iant over a function field $K$ with constant field of size an odd prime po
 wer $q$. Its $L$-function $L(T\,E/K)$ belongs to $1 + T\\mathbb{Z}[T]$. In
 spired by the algorithms of Schoof and Pila for computing zeta functions o
 f curves over finite fields\, we propose an approach to compute $L(T\,E/K)
 $. The idea is to compute\, for sufficiently many primes $\\ell$ coprime w
 ith $q$\, the reduction $L(T\,E/K) \\bmod{\\ell}$. The $L$-function is the
 n recovered via the Chinese remainder theorem. When $E(K)$ has a subgroup 
 of order $N \\geq 2$ coprime with $q$\, Chris Hall showed how to explicitl
 y calculate $L(T\,E/K) \\bmod{N}$. We present novel theorems going beyond 
 Hall's.\n
LOCATION:https://researchseminars.org/talk/UAANTS/27/
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