Factorization and arithmetic functions for orders in composition algebras

A well-known product, referred to as the Dirichlet convolution product, is generalized to arithmetic functions defined on an order in a Cayley division algebra. Factorization results for orders, multiplicative functions and analogues of the Moebius inversion formula are discussed.

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Bibliographic Details
Published in:Glasgow mathematical journal 1973-02, Vol.14 (1), p.86-95
Main Author: Lamont, P. J. C.
Format: Article
Language:English
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Summary:A well-known product, referred to as the Dirichlet convolution product, is generalized to arithmetic functions defined on an order in a Cayley division algebra. Factorization results for orders, multiplicative functions and analogues of the Moebius inversion formula are discussed.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089500001786