Using Goursat's lemma for groups, a simple representation and the invariant factor
decompositions of the subgroups of the group Zm× Zn are deduced, where m and n are …

Divisibility properties of random samples of integers | Revista de la Real Academia de Ciencias
Exactas, Físicas y Naturales. Serie A. Matemáticas Skip to main content SpringerLink Account …

We deduce an asymptotic formula with error term for the sum∑ n 1,…, nk≤ xf ([n 1,…, nk]),
where [n 1,…, nk] stands for the least common multiple of the positive integers n 1,…, nk (k≥ …

Menon's identity states that for every positive integer n one has∑(a− 1, n)= φ (n) τ (n), where
a runs through a reduced residue system (mod n),(a− 1, n) stands for the greatest common …

Let k≥ 2 be a fixed integer. We consider sums of type∑ n 1⋯ nk≤ x F (n 1,…, nk), taken
over the hyperbolic region {(n 1,…, nk)∈ N k: n 1⋯ nk≤ x}, where F: N k→ C is a given …

We derive a limit formula for higher convolutions of Ramanujan sums, generalizing an old
result of Carmichael. We then apply this in conjunction with the general theory of arithmetical …

We obtain asymptotic formulas with remainder terms for the hyperbolic summations ∑ _ mn
≤ xf ((m, n))∑ mn≤ xf ((m, n)) and ∑ _ mn ≤ xf (m, n)∑ mn≤ xf (m, n), where f belongs to …

1 Dirichlet law for factorisation of integers, polynomials and permutations Page 1 Math. Proc.
Camb. Phil. Soc.: page 1 of 28 1 doi:10.1017/S0305004123000427 Dirichlet law for …

We deduce asymptotic formulas for the sums∑ n 1,…, nr≤ xf (n 1⋯ nr) and∑ n 1,…, nr≤ xf
([n 1,…, nr]), where r≥ 2 is a fixed integer,[n 1,…, nr] stands for the least common multiple of …

We generalize certain recent results of Ushiroya concerning Ramanujan expansions of
arithmetic functions of two variables. We also show that some properties on expansions of …