Add to ORKGDenote by R+ and N the set of all positive real numbers and the natural numbers,respectively. Let P = {p1, . . . , pn, . . . } be the set of all primes enumerated inincreasing order. Denote by R(A, B) = {a b; a ? A, b ? B} the ratio set of A, B ? R+ and put R(A) = R(A, A) for A ? R+ (cf. [3],[4],[5]). Note that R(A, B) 6= R(B, A) in general, however R(A, B) is dense in R+ if and only if R(B, A) is dense in R+
Denote by P the set of all primes and by P (n) the largest prime factor of integer n 1 with the conv...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
International audienceIt is well known that the sequence $\varphi(n)/n$, n=1,2,... has a singular as...
summary:Let $\mathbb {P} = \lbrace p_1, p_2, \dots , p_i, \dots \rbrace $ be the set of prime number...
summary:Let $\mathbb {P} = \lbrace p_1, p_2, \dots , p_i, \dots \rbrace $ be the set of prime number...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
Consider a set $X\subseteq \mathbb{R}^d$ which is 1-dense, namely, it intersects every unit ball. We...
AbstractA monotonicity result for the ratio between two generalized logarithmic means is established...
Recently introduced by the authors in [Proc. Edinb. Math. Soc. 60 (2020), 139-167], quasi-densities ...
For a given monic integral polynomial $f(x)$ of degree $n$, we define local roots $r_i$ of $f(x)$ fo...
AbstractLet Pn denote the set of all algebraic polynomials of degree at most n with real coefficient...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractExtending a classical result of Erdős, we derive the following concise statement:Let r≥3 and...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractFor every positive integer n, let Xn′ be the set of primitive Dirichlet characters modulo n....
Denote by P the set of all primes and by P (n) the largest prime factor of integer n 1 with the conv...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
International audienceIt is well known that the sequence $\varphi(n)/n$, n=1,2,... has a singular as...
summary:Let $\mathbb {P} = \lbrace p_1, p_2, \dots , p_i, \dots \rbrace $ be the set of prime number...
summary:Let $\mathbb {P} = \lbrace p_1, p_2, \dots , p_i, \dots \rbrace $ be the set of prime number...
After the proof of Zhang about the existence of infinitely many bounded gaps between consecutive pri...
Consider a set $X\subseteq \mathbb{R}^d$ which is 1-dense, namely, it intersects every unit ball. We...
AbstractA monotonicity result for the ratio between two generalized logarithmic means is established...
Recently introduced by the authors in [Proc. Edinb. Math. Soc. 60 (2020), 139-167], quasi-densities ...
For a given monic integral polynomial $f(x)$ of degree $n$, we define local roots $r_i$ of $f(x)$ fo...
AbstractLet Pn denote the set of all algebraic polynomials of degree at most n with real coefficient...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
AbstractExtending a classical result of Erdős, we derive the following concise statement:Let r≥3 and...
AbstractA new expansion is given for partial sums of Eulerʼs pentagonal number series. As a corollar...
AbstractFor every positive integer n, let Xn′ be the set of primitive Dirichlet characters modulo n....
Denote by P the set of all primes and by P (n) the largest prime factor of integer n 1 with the conv...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
International audienceIt is well known that the sequence $\varphi(n)/n$, n=1,2,... has a singular as...