16:00
Pointwise bounds for 3-torsion (note: Wednesday)
Abstract
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 $h_3(d) \ll_\epsilon d^{1/3 + \epsilon}$. We will discuss how to improve this to $h_3(d) \ll d^{0.32}$. This is joint work with Peter Koymans.
We are pleased to announce that the Graduate School researcher training programme for Michaelmas term has now been finalised and is open for booking. Sessions are available free of charge to postgraduate students across the University. All training sessions are offered in hybrid format and can be joined either in person in the Graduate School Room in Rewley House (Wellington Square) or online through Teams.
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