The Möbius inversion and Fourier coefficients. (Q5931682)

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.