# Log-Coulomb gases in the projective line of a $p$-field

@inproceedings{Webster2021LogCoulombGI, title={Log-Coulomb gases in the projective line of a \$p\$-field}, author={Joseph B. Webster}, year={2021} }

This article extends recent results on log-Coulomb gases in a p-field K (i.e., a nonarchimedean local field) to those in its projective line P(K), where the latter is endowed with the PGL2invariant Borel probability measure and spherical metric. Our first main result is an explicit combinatorial formula for the canonical partition function of log-Coulomb gases in P(K) with arbitrary charge values. Our second main result is called the “(q+1)th Power Law”, which relates the grand canonical…

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