A GENERALIZED MOBIUS TRANSFORM, ARITHMETIC FOURIER-TRANSFORMS, AND PRIMITIVE ROOTS

A general approach to arithmetic Fourier transforms is developed. The implementation is based on sine and cosine ''killer'' procedures perta ining to a generalized Mobius transform involving reduced periodic mul tiplicative arithmetical functions, It is shown that cosine killer pro cedures exist whenever one half of Euler's totient function of the ord er of the transform is odd. Primitive roots and indices with respect t o primitive roots play an important part in the derivation of the resu lts.