On the radical of a perfect number.
On the Ramanujan AGM fraction. II: The complex-parameter case.
On the Rationality of Certain Generating Functions.
On the reducibility of binomial congruences and on the bound of the least integer belonging to a given exponent
On the relation between units and Jacobi sums in Prime cyclotomic Fields.
On the representation of an integer in two different bases.
On the representation of as .
On the Riesz means of n/ϕ(n) - III
Let ϕ(n) denote the Euler totient function. We study the error term of the general kth Riesz mean of the arithmetical function n/ϕ(n) for any positive integer k ≥ 1, namely the error term where . For instance, the upper bound for |Ek(x)| established here improves the earlier known upper bounds for all integers k satisfying .
On the roots of certain sequences of congruences
On the sequence .
On the set .
On the set of numbers {14, 22, 30, 42, 90}
On the set of values of the Euler function.
On the smallest pseudopower
On the solutions of .
On the special solutions of an equation in a finite field.
On the spectrum of the Thue-Morse quasicrystal and the rarefaction phenomenon
The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated by means of the Bombieri-Taylor conjecture, for Bragg peaks, and of a new conjecture that we call Aubry-Godrèche-Luck conjecture, for the singular continuous component. The decomposition of the Fourier transform of the weighted Dirac comb is obtained in terms of tempered distributions. We show that the asymptotic arithmetics of the -rarefied sums of the Thue-Morse sequence (Dumont; Goldstein, Kelly and Speer; Grabner;...
On the Square Factors of the Numbers of Fermat and Ferentinou-Nicolakopoulou
On the statistical properties of finite continued fractions.
On the structure of (−β)-integers
The (−β)-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. When β is the analogue of a Parry number, we describe the structure of the set of (−β)-integers by a fixed point of an anti-morphism.