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I came across this research profile where under Research Overview, it states that

These days C*-algebra theory is a very active area of mathematical research in its own right, and enjoys deep connections with other areas of mathematics such as symbolic dynamics, ergodic theory, group theory and even number theory.

My question is how C*-algebras and number theory are connected and if this is an active area of research?

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    $\begingroup$ While I appreciate your list was meant to be indicative not exhaustive, worth pointing out that there has been more recent work strengthening some of the earlier results: see arxiv.org/abs/1906.00445 which you could add to the list $\endgroup$ – Yemon Choi Jan 30 '20 at 14:29
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    $\begingroup$ thanks for the pointer; two 2019 references added, this might also go some way to answering the second question of the OP: "is this is an active area of research?" $\endgroup$ – Carlo Beenakker Jan 30 '20 at 14:41
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I think the most prominent example of this is Connes' work on the Riemann hypothesis from a C*-algebra perspective.

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