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Pointwise bounds for 3-torsion

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  • UserStephanie Chan (UCL)
  • ClockTuesday 17 February 2026, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Tim Santens .

For $\ell$ an odd prime number and $d$ a squarefree integer, a notable problem in arithmetic statistics is to give pointwise bounds for the size of the $\ell$-torsion of the class group of $\mathbb{Q}(\sqrt{d})$. This is in general a difficult problem, and unconditional pointwise bounds are only available for $\ell = 3$ due to work of Pierce, Helfgott–Venkatesh and Ellenberg–Venkatesh. The current record due to Ellenberg–Venkatesh is $h_3(d) \ll_{\epsilon} d1/3 + \epsilon$. We will discuss how to improve this to $h_3(d) \ll d^{0.32}$. This is joint work with Peter Koymans.

This talk is part of the Number Theory Seminar series.

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