Regular coverings of the integers by arithmetic progressions
Regular maps in generalized number systems
Rekurrente Folgen mit lokal gleichmäßig beschränkter Primteileranzahl
Relations among arithmetical functions, automatic sequences, and sum of digits functions induced by certain Gray codes
In the study of the -adic sum of digits function , the arithmetical function and for plays a very important role. In this paper, we firstly generalize the relation between and to a bijective relation between arithmetical functions. And as an application, we investigate some aspects of the sum of digits functions induced by binary infinite Gray codes . We can show that the difference of the sum of digits function, , is realized by an automaton. And the summation formula of the sum...
Remark on multiplicative functions.
Remarks on arithmetical functions .
Remarks on generalized Ramanujan sums and even functions.
Remarks on maximum and minimum exponents in factoring
Remarks on number theory I. On primitive α-abundant numbers
Remarks on number theory II. Some problems on the σ function
Remarks on Ramanujan's inequality concerning the prime counting function
In this paper we investigate Ramanujan’s inequality concerning the prime counting function, asserting that for sufficiently large. First, we study its sharpness by giving full asymptotic expansions of its left and right hand sides expressions. Then, we discuss the structure of Ramanujan’s inequality, by replacing the factor on its right hand side by the factor for a given , and by replacing the numerical factor by a given positive . Finally, we introduce and study inequalities analogous...
Remarks on self-affine tilings.
Remarks on some number-theoretical functional equations.
Remarks on Steinhaus’ property and ratio sets of sets of positive integers
This paper is closely related to an earlier paper of the author and W. Narkiewicz (cf. [7]) and to some papers concerning ratio sets of positive integers (cf. [4], [5], [12], [13], [14]). The paper contains some new results completing results of the mentioned papers. Among other things a characterization of the Steinhaus property of sets of positive integers is given here by using the concept of ratio sets of positive integers.
Remarks on systems of congruence classes
Remarks on the paper "Sur certaines hypothèses concernant les nombres premiers"
Remarks on the structure of the multiplicative monoid of integers modulo m.
Remarks to the paper of the E. Cohen "Arithmetical functions associated with arbitrary sets of integers"
Remarque au sujet de la fonction qui exprime la somme des diviseurs de .
Remarques sur la théorie des nombres et sur les fractions continues.