Representation of Arithmetic Functions and Free Probability - Brossura

CHO, ILWOO; Jorgensen, Palle

 
9783659385698: Representation of Arithmetic Functions and Free Probability

Sinossi

In this monograph, we study a class of representations of arithmetic functions, and corresponding operator-theoretic and free-probabilistic properties. We associate given arithmetic functions to certain matrices, and study free-probabilistic structures on such matrices determined by prime-powers. By understanding such matrices as operators acting on an “indefinite” inner product space, we derive operator-theoretic properties of them. This study is one of the frontier works, providing connections between modern number theory, and operator theory, via free probability with help of representation theory.

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L'autore

Ilwoo Cho: Ph.D. Professor of St. Ambrose Univ., Dept. of Math. & Stat., Palle E. T. Jorgensen: Ph.D. Professor of Univ. of Iowa, Dept. of Math.

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