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

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Ilwoo Cho & Palle Jorgensen, 2019. "Primes in Intervals and Semicircular Elements Induced by p -Adic Number Fields Q p over Primes p," Mathematics, MDPI, vol. 7(2), pages 1-35, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:199-:d:207389
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