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

Ilwoo Cho and Palle Jorgensen
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Ilwoo Cho: Department of Mathematics & Statistics, Saint Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USA
Palle Jorgensen: Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA 52242, USA

Mathematics, 2019, vol. 7, issue 2, 1-35

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 .

Keywords: free probability; primes; p-adic number fields; Banach *-probability spaces; weighted-semicircular elements; semicircular elements; truncated linear functionals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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