• Alexandru Zaharescu

Articles written in Proceedings – Mathematical Sciences

• Irreducibility results for compositions of polynomials in several variables

We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions of polynomials.

• Derivations and Generating Degrees in the Ring of Arithmetical Functions

In this paper we study a family of derivations in the ring of arithmetical functions of several variables over an integral domain, and compute the generating degrees of the ring of arithmetical functions over the kernel of these derivations.

• Real Moments of the Restrictive Factor

Let 𝜆 be a real number such that $0 &lt; \lambda &lt; 1$. We establish asymptotic formulas for the weighted real moments $\sum_{n\leq x}R^\lambda(n)(1-n/x)$, where $R(n)=\prod^k_{v=1}p^{\alpha v-1}_v$ is the Atanassov strong restrictive factor function and $n=\prod^k_{v=1}p^{\alpha v}_v$ is the prime factorization of 𝑛.

• Irreducible Multivariate Polynomials Obtained from Polynomials in Fewer Variables, II

We provide several irreducibility criteria for multivariate polynomials and methods to construct irreducible polynomials starting from irreducible polynomials in fewer variables.

• Irrational factor races

We investigate the behavior of the sum of the irrational factor function over arithmetic progressions. We first establish a general asymptotic formula for such a sum, and then obtain some further results in the case of arithmetic progressions $3n\pm 1$.

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019