Representation of Arithmetic Functions and Free Probability

By ILWOO CHO

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.

• Format: Paperback
• Language: English
• ISBN: 3659385697
• ISBN13: 9783659385698
• Release Date: September 2015
• Publisher: LAP Lambert Academic Publishing
• Length: 92 Pages
• Weight: 0.32 lbs.
• Dimensions: 0.2" x 6.0" x 9.0"