Arithmetic functions over rings with zero divisors.
Arithmetic Subseries of Series with Multiplicative Terms
Arithmetical aspects of certain functional equations
The classical system of functional equations (n ∈ ℕ) with s ∈ ℂ, investigated for instance by Artin (1931), Yoder (1975), Kubert (1979), and Milnor (1983), is extended to (n ∈ ℕ) with complex valued sequences . This leads to new results on the periodic integrable and the aperiodic continuous solutions F:ℝ₊ → ℂ interrelating the theory of functional equations and the theory of arithmetic functions.
Arithmetical consequences of two identities of B. Gordon.
Arithmetical functions associated with arbitrary sets of integers
Arithmetical functions on a locally finite, locally semi-modular, local lattice.
Arithmetical identities of the Brauer-Rademacher type.
Arithmetical sequences and systems of functional equations.
Arithmetical sums in regular convolutions.
Arithrnetical Notes, VII Sorne Classes of even Functions (mod r).
Asymptotic estimates for phi functions for subsets of .
Asymptotic formulae concerning arithmetical functions defined by cross-convolutions. VI: --free integers.
Automorphisms of a Finite P-Group
Average order in cyclic groups
For each natural number we determine the average order of the elements in a cyclic group of order . We show that more than half of the contribution to comes from the primitive elements of order . It is therefore of interest to study also the function . We determine the mean behavior of , , , and also consider these functions in the multiplicative groups of finite fields.
Average orders of multiplicative arithmetical functions of integer matrices
Befreundete Zahlen mit gegebener Primteileranzahl.
Bemerkung zu einem Ergebnis von Erdös über befreundete Zahlen.
Bemerkungen über die von Gauss mit [x] bezeichnete arithmetische Function einer reellen Grösse x.
Bemerkungen über Zulässigkeitsmengen vollständig additiver Funktionen.
Bounds for frequencies of residues of second-order recurrences modulo
The authors examine the frequency distribution of second-order recurrence sequences that are not -regular, for an odd prime , and apply their results to compute bounds for the frequencies of -singular elements of -regular second-order recurrences modulo powers of the prime . The authors’ results have application to the -stability of second-order recurrence sequences.