tailieunhanh - Rational arithmetical functions related to certain unitary analogs of GCD type matrices
An arithmetical function f is a rational arithmetical function of order (r, s) if it can be written as the Dirichlet convolution of r completely multiplicative functions and s inverses of completely multiplicative functions. In this paper we show that pseudo-unitarily semimultiplicative functions and a related generalization of the unitary analog of Euler’s totient function are rational arithmetical functions of orders (1, 2) and (2, 3). These functions arise from the theory the so-called pseudo-LCUM and GCUD reciprocal pseudo-LCUM matrices, where GCUD and pseudoLCUM stand for the greatest common unitary divisor and an extension of the least common unitary multiple. |
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