Recurrences and Legendre transform.
Recurrences for the Bernoulli and Euler numbers.
Recurrent versus diffusive dynamics for a kicked quantum oscillator
Reducibility and irreducibility of Stern -polynomials
The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials defined by , , , and ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that can only have simple zeros, and we state a...
Reducing a set by subtracting squares.
Regular coverings of the integers by arithmetic progressions
Regular h-ranges and weakly pleasant h-bases.
Regular maps in generalized number systems
Regular sets and conditional density: an extension of Benford's law
We give an extension of Benford's law (first digit problem) by using the concept of conditional density, introduced by Fuchs and Letta. The main tool is the notion of regular subset of integers.
Regularity and irregularity of sequences generated by automata
Regularity properties of the Stern enumeration of the rationals.
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...
Relations among Fourier coefficients of certain eta products.
Relations between the reciprocal sum and the alternating sum for generalized Lucas numbers.
Relations de récurrence modulo m
Remarks on maximum and minimum exponents in factoring
Remarks on number theory III. On addition chains
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 sum of products of -twisted Euler polynomials and numbers.