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Krein-Space Representations of Arithmetic Functions Determined by Primes

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In this paper, we study representations of the algebra \(\mathcal {A}\) generated by all arithmetic functions, determined by fixed primes (or prime numbers). The main purposes of this paper are (i) to establish nice representational models of \(\mathcal {A}\) under primes, (ii) to study fundamental properties of such representations, (iii) to investigate how \( \mathcal {A}\) is acting as operators in representations, and (iv) to consider new free probability models on Krein-space operator algebras.

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Authors and Affiliations

  1. Department of Mathematics, St. Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA, 52803, USA

    Ilwoo Cho & Palle E. T. Jorgensen

  2. Department of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA, 52242, USA

    Ilwoo Cho & Palle E. T. Jorgensen

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  1. Ilwoo Cho
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  2. Palle E. T. Jorgensen
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Correspondence to Ilwoo Cho.

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Presented by Peter Littelmann.

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Cho, I., Jorgensen, P.E.T. Krein-Space Representations of Arithmetic Functions Determined by Primes. Algebr Represent Theor 17, 1809–1841 (2014). https://doi.org/10.1007/s10468-014-9473-z

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