Ramanujan expansions of multiplicative functions
Ramanujan sums and almost periodic functions
Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood
We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility...
Ramdom variables related to distributions of sums modulo an integer.
Random generators and normal numbers.
Rauzy tilings and bounded remainder sets on the torus.
Recouvrement d'un cercle par des intervalles
Recouvrement optimal du cercle par les multiples d'un intervalle
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.
Regularities of distribution
Regularity of distribution of (nα)-sequences
Relative Gleichverteilung in lokalkompakten Räumen II.
Remark to a theorem of P. Erdös
Remarks on Invariant Measures for Number Theoretic Transformations.
Remarks on several types of convergence of bounded sequences
In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, -convergence, -convergence, almost convergence, strong -Cesàro convergence and uniformly strong -Cesàro convergence.
Remarks on statistical independence of sequences
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 the Ergodic Theory of the Continued Fractions
Remarks on the -density of sets of numbers. II
Remarks on the theorem of Elliott and Daboussi, and applications