Number fields: certifying class groups and regulators

[tb65536]

The purpose of this project would be to use the analytic class number formula to certify class groups and regulators of number fields.

[b-mehta]

I'm interested in working on this.

[Multramate]

I'm guessing Alain's talk on Wednesday will be very much related to this, so you should talk to him.

[tb65536]

Regarding rigorous approximation of the residue of Dedekind zeta, this 2013 paper is a nice survey of the various options: https://arxiv.org/abs/1305.0035

In particular, if we want to use the partial product in Cohen's book, then the relevant paper would be Bach's paper "Improved approximations for Euler products" (which seems rather tricky to get ahold of, but the relevant bound is also written out in this paper: https://eprint.iacr.org/2025/1514.pdf).