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The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series of the form ζ 2(s)ζ(2s−1)ζ M(2s)H(s), where M is an arbitrary integer and H(s) has an Euler product which converges absolutely for R s > σ0, with some fixed σ0 < 1/2.

On a system of equations with primes

Paolo Leonetti, Salvatore Tringali (2014)

Journal de Théorie des Nombres de Bordeaux

Given an integer $n \geq 3$ , let $u_{1}, ..., u_{n}$ be pairwise coprime integers $\geq 2$ , $𝒟$ a family of nonempty proper subsets of ${1, ..., n}$ with “enough” elements, and $ε$ a function $𝒟 \to {\pm 1}$ . Does there exist at least one prime $q$ such that $q$ divides $\prod_{i \in I} u_{i} - ε (I)$ for some $I \in 𝒟$ , but it does not divide $u_{1} \dots u_{n}$ ? We answer this question in the positive when the $u_{i}$ are prime powers and $ε$ and $𝒟$ are subjected to certain restrictions.We use the result to prove that, if $ε_{0} \in {\pm 1}$ and $A$ is a set of three or more primes that contains all prime divisors of any number of the form $\prod_{p \in B} p - ε_{0}$ for...

On an algorithm which produces the g.c.d. of a set of n (n>2) integers in a simultaneous manner.

P. Laborde (1967)

Gaceta Matemática

On an extension of Kronecker's function

Rao, K. Nageswara (1968)

Portugaliae mathematica

On certain arithmetic functions involving the greatest common divisor

Ekkehard Krätzel, Werner Nowak, László Tóth (2012)

Open Mathematics

The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.

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O číslech spřízněných a dokonalých. [II.]

O dělitelnosti čísel dekadických jedenácti

O jednom zovšeobecnení číselnoteoretického vzťahu $[a_{1}, a_{2}] = a_{1} a_{2} / (a_{1}, a_{2})$ a jeho použití

O multiplikatívnej pologrupe zvyškových tried (mod $m$ )

O postupnostiach prirodzených čísel s ohraničeným počtom prvočíselných deliteľov

On a compositeness test for $(2^{p} + 1) / 3$ .

On a conjecture of R. L. Graham

On a conjecture of R. L. Graham

On a problem of R.L.Graham

On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions

On a system of equations with primes

On an algorithm which produces the g.c.d. of a set of n (n>2) integers in a simultaneous manner.

On an extension of Kronecker's function

On certain arithmetic functions involving the greatest common divisor

On divisibility of some power sums.

On exceptions to Szegedy's theorem

On $f$ -thin sets

On happy factorizations.

On K-Stage Euclidean algorithms for Galois extensions of Q.

On multiplicatively e-perfect numbers.

Currently displaying 1 – 20 of 32