AbstractIn an article in Astérisque in 1979 Erdős conjectured the existence of a critical value α0∈(1,∞) such that if A(d,α) denotes the density of the integers having a divisor D, D≡1 (mod d), 1<D<exp(dα), then A(d,α)→0 or 1 as d→∞ according as α is less than, or greater than α0. This is proved, and α0 determined
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
For integer $n$ and real $u$, define $\Delta(n,u):= |\{d : d \mid n,\,{\rm e}^u <d\leqslant {\rm e}^...
AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the...
AbstractIn an article in Astérisque in 1979 Erdős conjectured the existence of a critical value α0∈(...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
AbstractThis note is a sequel to an earlier paper of the same title that appeared in this journal. W...
AbstractThe condition Σk<x|Σn<x (χ(n) − z)4Ω(n)n| = o(√logx), where Ω(n) stands for the number of pr...
We study the extent to which divisors of a typical integer $n$ are concentrated. In particular, defi...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
AbstractIn 1966 P. Erdös proved the following theorem:Let B = {bi: 1 < b1 < b2 < b3 < …} be an infin...
AbstractAn elementary construction of a sequence of positive integers is given. The sequence settles...
AbstractWe consider the coefficients dnj(y) in {((1 + z)x(1 − z)x − 1)}y = ∑n=0∞ zn ∑j = 0n, dnj(y)x...
AbstractLet A be an infinite sequence of positive integers a1 < a2 <… and put fA(x) = Σa∈A, a≤x(1a),...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
For integer $n$ and real $u$, define $\Delta(n,u):= |\{d : d \mid n,\,{\rm e}^u <d\leqslant {\rm e}^...
AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the...
AbstractIn an article in Astérisque in 1979 Erdős conjectured the existence of a critical value α0∈(...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
AbstractThis note is a sequel to an earlier paper of the same title that appeared in this journal. W...
AbstractThe condition Σk<x|Σn<x (χ(n) − z)4Ω(n)n| = o(√logx), where Ω(n) stands for the number of pr...
We study the extent to which divisors of a typical integer $n$ are concentrated. In particular, defi...
AbstractWe prove in a strong form an old conjecture of Erdös to the effect that ∑1⩽i<j⩽T(n)(dj−di)−1...
AbstractIn 1966 P. Erdös proved the following theorem:Let B = {bi: 1 < b1 < b2 < b3 < …} be an infin...
AbstractAn elementary construction of a sequence of positive integers is given. The sequence settles...
AbstractWe consider the coefficients dnj(y) in {((1 + z)x(1 − z)x − 1)}y = ∑n=0∞ zn ∑j = 0n, dnj(y)x...
AbstractLet A be an infinite sequence of positive integers a1 < a2 <… and put fA(x) = Σa∈A, a≤x(1a),...
AbstractThe number defined by the title is denoted by Ψ(x, y). Let u = log xlog y and let ϱ(u) be th...
AbstractWe show that for A ranging over n×n circulants with three ones in each row, where n is prime...
AbstractWe define h(n) to be the largest function of n such that from any set of n nonzero integers,...
For integer $n$ and real $u$, define $\Delta(n,u):= |\{d : d \mid n,\,{\rm e}^u <d\leqslant {\rm e}^...
AbstractIn this paper we prove (in a rather more precise form) two conjectures of P. Erdös about the...
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