RésuméLet 1=d1(n)<d2(n)<…<dτ(n)=nbe the sequence of all the divisors of the integernin increasing order. Let us say that the divisors ofnarez-dense iff max1⩽i<τ(n)di+1(n)/di(n)⩽zand letD(x, z) be the number of positive integers ⩽xwhose divisors arez-dense. Our major result here is an improvement of an estimate of Tenenbaum obtained by showing thatc1xlogz/logx⩽D(x, z)⩽c2xlogz/logxforx⩾z⩾2 and suitable positive constantsc1andc2
AbstractLet σα(n) be the sum of the αth power of the positive divisors of n. We establish an asympto...
Abstract. Rényi’s result on the density of integers whose prime factorizations have excess multipli...
Abstract. A partition of a positive integer n is a finite sequence of positive integers a1, a2,..., ...
RésuméLet 1=d1(n)<d2(n)<…<dτ(n)=n be the sequence of all the divisors of the integer n in increasing...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
AbstractThe condition Σk<x|Σn<x (χ(n) − z)4Ω(n)n| = o(√logx), where Ω(n) stands for the number of pr...
We estimate the density of integers which have more than one divisor in an interval (y, z] with z ≈ ...
This dissertation deals with four problems concerning arithmetic structures in dense sets of integer...
71 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.We investigate several problem...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
Let (Fn)n be the sequence of Fibonacci numbers. The order of appearance (in the Fibonacci sequence) ...
We consider a uniformly bounded sequence c_j(l) of positive numbers depending on a parameter L. They...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractThe primary objective of this paper is to extend the results of N. Romanoff (Math. Ann. 109,...
AbstractLet σα(n) be the sum of the αth power of the positive divisors of n. We establish an asympto...
Abstract. Rényi’s result on the density of integers whose prime factorizations have excess multipli...
Abstract. A partition of a positive integer n is a finite sequence of positive integers a1, a2,..., ...
RésuméLet 1=d1(n)<d2(n)<…<dτ(n)=n be the sequence of all the divisors of the integer n in increasing...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
AbstractLet 1=d1(n)<d2(n)<⋯<dτ(n)=n be the sequence of all positive divisors of the integer n in inc...
AbstractThe condition Σk<x|Σn<x (χ(n) − z)4Ω(n)n| = o(√logx), where Ω(n) stands for the number of pr...
We estimate the density of integers which have more than one divisor in an interval (y, z] with z ≈ ...
This dissertation deals with four problems concerning arithmetic structures in dense sets of integer...
71 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.We investigate several problem...
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd
Let (Fn)n be the sequence of Fibonacci numbers. The order of appearance (in the Fibonacci sequence) ...
We consider a uniformly bounded sequence c_j(l) of positive numbers depending on a parameter L. They...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractThe primary objective of this paper is to extend the results of N. Romanoff (Math. Ann. 109,...
AbstractLet σα(n) be the sum of the αth power of the positive divisors of n. We establish an asympto...
Abstract. Rényi’s result on the density of integers whose prime factorizations have excess multipli...
Abstract. A partition of a positive integer n is a finite sequence of positive integers a1, a2,..., ...
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