The Bounded Cohomology of SL2 Over Local Fields and S-Integers

Nicolas Monod
2019
Article

Résumé

It is proved that the continuous bounded cohomology of SL2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing for SL2 over S-integers.

Source officielle

https://infoscience.epfl.ch/record/267881?ln=fr

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Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

The Bounded Cohomology of SL2 Over Local Fields and S-Integers

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Moments of the number of points in a bounded set for number field lattices