Next Article in Journal
Stability Analysis of a Fractional-Order Linear System Described by the Caputo–Fabrizio Derivative
Previous Article in Journal
Convergence Analysis of Weighted-Newton Methods of Optimal Eighth Order in Banach Spaces
Previous Article in Special Issue
The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach
Article Menu
Issue 2 (February) cover image

Export Article

Open AccessArticle
Mathematics 2019, 7(2), 199; https://doi.org/10.3390/math7020199

Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields Q p over Primes p

1
Department of Mathematics & Statistics, Saint Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
2
Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA 52242, USA
*
Author to whom correspondence should be addressed.
Received: 11 December 2018 / Revised: 12 February 2019 / Accepted: 15 February 2019 / Published: 19 February 2019
(This article belongs to the Special Issue Mathematical Physics II)
Full-Text   |   PDF [489 KB, uploaded 21 February 2019]

Abstract

In this paper, we study free probability on (weighted-)semicircular elements in a certain Banach *-probability space ( LS , τ 0 ) induced by measurable functions on p-adic number fields Q p over primes p . In particular, we are interested in the cases where such free-probabilistic information is affected by primes in given closed intervals of the set R of real numbers by defining suitable “truncated” linear functionals on LS . View Full-Text
Keywords: free probability; primes; p-adic number fields; Banach *-probability spaces; weighted-semicircular elements; semicircular elements; truncated linear functionals free probability; primes; p-adic number fields; Banach *-probability spaces; weighted-semicircular elements; semicircular elements; truncated linear functionals
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Cho, I.; Jorgensen, P. Primes in Intervals and Semicircular Elements Induced by p-Adic Number Fields Q p over Primes p. Mathematics 2019, 7, 199.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top