Alexandru Zaharescu
Articles written in Proceedings – Mathematical Sciences
Volume 115 Issue 2 May 2005 pp 117-126
Irreducibility results for compositions of polynomials in several variables
Anca Iuliana Bonciocat Alexandru Zaharescu
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.
Volume 117 Issue 2 May 2007 pp 167-175
Derivations and Generating Degrees in the Ring of Arithmetical Functions
Alexandru Zaharescu Mohammad Zaki
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.
Volume 119 Issue 4 September 2009 pp 559-566
Real Moments of the Restrictive Factor
Andrew Ledoan Alexandru Zaharescu
Let 𝜆 be a real number such that $0 < \lambda < 1$. 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.
Volume 121 Issue 2 May 2011 pp 133-141
Irreducible Multivariate Polynomials Obtained from Polynomials in Fewer Variables, II
Nicolae Ciprian Bonciocat Alexandru Zaharescu
We provide several irreducibility criteria for multivariate polynomials and methods to construct irreducible polynomials starting from irreducible polynomials in fewer variables.
Volume 124 Issue 4 November 2014 pp 471-479
Sneha Chaubey Milenda Lanius Alexandru Zaharescu
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 $3n\pm 1$.
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