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SUMMARY:Jane Shi (MIT)
DTSTART:20251124T210000Z
DTEND:20251124T220000Z
DTSTAMP:20260423T035958Z
UID:NTBU/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/36/">Li
 fting $L$-polynomials of genus 2 curves</a>\nby Jane Shi (MIT) as part of 
 Boston University Number Theory Seminar\n\nLecture held in CDS Room 548 in
  Boston University.\n\nAbstract\nLet $C$ be a genus $2$ curve over $\\math
 bb{Q}$. For each odd prime $p$\nof good reduction\, we denote the numerato
 r \nof the zeta function of $C$ at $p$ by $L_p(T)$.\n\nHarvey and Sutherla
 nd's \nimplementation of Harvey's average polynomial-time algorithm comput
 es \n$L_p(T) \\bmod \\ p$ for all good primes $p\\leq B$ in $O(B\\log^{3+o
 (1)}B)$ time\, which is \n$O(\\log^{4+o(1)} p)$ time on average per prime.
 \nAlternatively\, their algorithm can do this for a single good prime \n$p
 $ in $O(p^{1/2}\\log^{1+o(1)}p)$ time. While Harvey's algorithm \ncan also
  be used to compute the full zeta function\, no practical implementation \
 nof this step currently exists.\n\n\nIn this talk\, I will present an $O(\
 \log^{2+o(1)}p)$ Las Vegas algorithm that \ntakes the $\\bmod \\ p$ output
  of Harvey and Sutherland's implementation and \ncomputes the full zeta fu
 nction. I will also show benchmark results \ndemonstrating substantial spe
 edups compared to the fastest\nalgorithms currently available for computin
 g the full zeta function of a genus $2$ curve.\n
LOCATION:https://researchseminars.org/talk/NTBU/36/
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