Ramanujan primes: bounds, runs, twins, and gaps.
Rekurrente Folgen mit lokal gleichmäßig beschränkter Primteileranzahl
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 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 paper "Sur certaines hypothèses concernant les nombres premiers"
Representation of a prime as the sum of squares in a tower of fields.
Representing integers as linear combinations of S-units
Retour sur la méthode de Čebyšev dans la théorie des nombres premiers