# Journal of the Ramanujan Mathematical Society

Volume 35, Issue 1, March 2020 pp. 35–69.

Free poisson elements induced by semicircular elements from analysis on p-adic number fields Qp over primes p

**Authors**:
Ilwoo Cho and Hemen Dutta

**Author institution:**421 Ambrose Hall, Saint Ambrose Univ., Dept. of Math. & Stat., 518 W. Locust St., Davenport, Iowa, 52803, U.S.A.

**Summary: **
In this paper, we construct-and-study free (weighted-)Poisson
elements in the Banach *-probability space (LS, τ
0), generated by mutually free semicircular elements {Θ
{p,j}}{p ∈ P, j ∈ Z induced by measurable
functions on the p-adic number fields Q p, for all p
in the set P of all primes, and for all j in the set
Z of all integers. In~particular, we are interested in
free Poisson elements generated by certain free random
variables of (LS, τ 0) induced by semicircular elements.

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