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SUMMARY:Stephanie Chan (University College London)
DTSTART:20260121T160000Z
DTEND:20260121T170000Z
DTSTAMP:20260418T065926Z
UID:LNTS/180
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/180/">P
 ointwise bounds for 3-torsion</a>\nby Stephanie Chan (University College L
 ondon) as part of London number theory seminar\n\nLecture held in Room 505
 \, UCL Maths building\, 25 Gordon Street.\n\nAbstract\nFor $\\ell$ an odd 
 prime number and $d$ a squarefree integer\, a notable problem in arithmeti
 c statistics is to give pointwise bounds for the size of the $\\ell$-torsi
 on of the class group of $\\mathbb{Q}(\\sqrt{d})$. This is in general a di
 fficult problem\, and unconditional pointwise bounds are only available fo
 r $\\ell = 3$ due to work of Pierce\, Helfgott–Venkatesh and Ellenberg
 –Venkatesh. The current record due to Ellenberg–Venkatesh is $h_3(d) \
 \ll_\\epsilon d^{1/3 + \\epsilon}$. We will discuss how to improve this to
  $h_3(d) \\ll d^{0.32}$. This is joint work with Peter Koymans.\n
LOCATION:https://researchseminars.org/talk/LNTS/180/
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