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SUMMARY:Pointwise bounds for 3-torsion - Stephanie Chan (UCL)
DTSTART:20260217T143000Z
DTEND:20260217T153000Z
UID:TALK242806@talks.cam.ac.uk
CONTACT:Tim Santens
DESCRIPTION:For $\\ell$ an odd prime number and $d$ a squarefree integer\,
  a notable problem in arithmetic statistics is to give pointwise bounds fo
 r the size of the $\\ell$-torsion of the class group of $\\mathbb{Q}(\\sqr
 t{d})$. This is in general a difficult problem\, and unconditional pointwi
 se bounds are only available for $\\ell = 3$ due to work of Pierce\, Helfg
 ott–Venkatesh and Ellenberg–Venkatesh. The current record due to Ellen
 berg–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:MR13
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