The Möbius inversion and Fourier coefficients. (English) Zbl 1034.11006
The authors show that an analogue of the Möbius inversion formula in a commutative semigroup with unique factorization can be used to study \(n\)-dimensional Fourier coefficients. The authors utilize to this aim an arbitrary algebraic number field of degree \(n\), whose ring of integers is a unique factorization domain. The authors do not mention that the existence of such fields for large \(n\) is still doubtful.
Reviewer: Wladyslaw Narkiewicz (Wrocław)
MSC:
| 11A25 | Arithmetic functions; related numbers; inversion formulas |
| 20M14 | Commutative semigroups |
| 65T50 | Numerical methods for discrete and fast Fourier transforms |
| 11R04 | Algebraic numbers; rings of algebraic integers |
| 13F15 | Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) |
| 42B05 | Fourier series and coefficients in several variables |
Keywords:
arithmetic Fourier transform; algebraic integers; Möbius inversion; arithmetical semigroupsReferences:
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