# 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…

## References

SHOWING 1-10 OF 10 REFERENCES

Functional equations for zeta functions of groups and rings

- Mathematics
- 2006

We introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations.…

The importance of the Selberg integral

- Mathematics
- 2007

It has been remarked that a fair measure of the impact of Atle Selberg’s work is the number of mathematical terms that bear his name. One of these is the Selberg integral, an n-dimensional…

The Probability That a Random Monic p-adic Polynomial Splits

- MathematicsExp. Math.
- 2006

It is shown that rn satisfies an interesting recursion, a conjecture on the asymptotic behavior of rn as n goes to infinity is made, and the conjecture in the case that the residue field has two elements is proved.

Energy integrals over local fields and global height bounds

- Mathematics, Computer Science
- 2013

Lower bounds set by Bombieri and Zannier for the limit infimum of the Weil height in fields of totally p-adic numbers and generalizations thereof are improved and combined with similar bounds at the archimedean places for totally real fields.

The combinatorics of log-Coulomb gases in p-fields

- Ph.D. thesis, Eugene,
- 2021

log-Coulomb Gas with Norm-Density in $$p$$-Fields

- Physics
- 2020

The main result of this paper is a formula for the integral $$\int_{K^N}\rho(x)\big(\max_{i 0$ represent the charges of an $N$-particle log-Coulomb gas in $K$ with background density $\rho$ and…

Non-Archimedean Electrostatics, arXiv e-prints (2020), arXiv:2002.07121

- 2002

Basic number theory, Classics in Mathematics, Springer-Verlag, Berlin

- MR 1344916 Joe Webster Department of Mathematics,
- 1995

A functional equation of Igusa’s local zeta function, Amer

- J. Math
- 1991