AbstractFor k a non-negative integer, let Pk(n) denote the kth largest prime factor of n where P0(n) = +∞ and if the number of prime factors of n is less than k, then Pk(n) = 1. We shall study the asymptotic behavior of the sum Ψk(x, y; g) = Σ1 ≤ n ≤ x, Pk(n) ≤ yg(n), where g(n) is an arithmetic function satisfying certain general conditions regarding its behavior on primes. The special case where g(n) = μ(n), the Möbius function, is discussed as an application
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
82 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.Integers without large prime f...
Let k ≥ 2 and ai, bi(1 ≤ i ≤ k) be integers such that ai > 0 and ∏1 ≤ i < j ≤ k (ai bj - aj bi) ≠ 0....
AbstractFor k a non-negative integer, let Pk(n) denote the kth largest prime factor of n where P0(n)...
Copyright c © 2014 Rafael Jakimczuk. This is an open access article distributed under the Creative C...
Copyright c © 2013 Rafael Jakimczuk. This is an open access article distributed under the Creative C...
Abstract. We use the saddle-point method (due to Hildebrand–Tenen-baum [3]) to study the asymptotic ...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
A primitive set is one in which no element of the set divides another. Erdős conjectured that the su...
Let p(n) denote the smallest prime factor of an integer n>1 and let p(1)=[infinity]. We study the...
In classical prime number theory there are several asymptotic formulas said to be “equivalent” to th...
We study the problem of bounding the number of primes p ≤ x in an arithmetic progression for which t...
AbstractWe study in this paper a new duality identity between large and small prime factors of integ...
concerning the upper est’imate of.&f(n) = max N(12,x) = max j 2 p(d) /. * t din d<z Previo...
AbstractFor an integer n >- 2, let P(n) be the largest prime factor of n. For an arbitrary strongly ...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
82 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.Integers without large prime f...
Let k ≥ 2 and ai, bi(1 ≤ i ≤ k) be integers such that ai > 0 and ∏1 ≤ i < j ≤ k (ai bj - aj bi) ≠ 0....
AbstractFor k a non-negative integer, let Pk(n) denote the kth largest prime factor of n where P0(n)...
Copyright c © 2014 Rafael Jakimczuk. This is an open access article distributed under the Creative C...
Copyright c © 2013 Rafael Jakimczuk. This is an open access article distributed under the Creative C...
Abstract. We use the saddle-point method (due to Hildebrand–Tenen-baum [3]) to study the asymptotic ...
We introduce explicit bounds for the sum 2≤n≤x 1/pi(n), where pi(n) is the number of primes that are...
A primitive set is one in which no element of the set divides another. Erdős conjectured that the su...
Let p(n) denote the smallest prime factor of an integer n>1 and let p(1)=[infinity]. We study the...
In classical prime number theory there are several asymptotic formulas said to be “equivalent” to th...
We study the problem of bounding the number of primes p ≤ x in an arithmetic progression for which t...
AbstractWe study in this paper a new duality identity between large and small prime factors of integ...
concerning the upper est’imate of.&f(n) = max N(12,x) = max j 2 p(d) /. * t din d<z Previo...
AbstractFor an integer n >- 2, let P(n) be the largest prime factor of n. For an arbitrary strongly ...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
82 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.Integers without large prime f...
Let k ≥ 2 and ai, bi(1 ≤ i ≤ k) be integers such that ai > 0 and ∏1 ≤ i < j ≤ k (ai bj - aj bi) ≠ 0....
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