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1
Content available remote

The number of squarefull numbers in an interval

100%
Liu H.-Q.
Acta Arithmetica
|
1993
|
tom 64
|
nr 2
129-149
2
Content available remote

The greatest prime factor of the integers in an interval

100%
Liu H.-Q.
Acta Arithmetica
|
1993
|
tom 65
|
nr 4
301-328
3
Content available remote

On some divisor problems

100%
Liu H.-Q.
Acta Arithmetica
|
1994
|
tom 68
|
nr 2
193-200
4
Content available remote

Divisor problems of 4 and 3 dimensions

100%
Liu H.-Q.
Acta Arithmetica
|
1995
|
tom 73
|
nr 3
249-269
5
Content available remote

The distribution of 4-full numbers

100%
Liu H.-Q.
Acta Arithmetica
|
1994
|
tom 67
|
nr 2
165-176
6
Content available remote

On the estimates of double exponential sums

100%
Liu H.-Q.
Acta Arithmetica
|
2007
|
tom 129
|
nr 3
203-247
7
Content available remote

On the number of abelian groups of a given order (supplement)

100%
Liu H.-Q.
Acta Arithmetica
|
1993
|
tom 64
|
nr 3
285-296
EN
1. Introduction. The aim of this paper is to supply a still better result for the problem considered in [2]. Let A(x) denote the number of distinct abelian groups (up to isomorphism) of orders not exceeding x. We shall prove Theorem 1. For any ε > 0, $A(x) = C₁x + C₂x^{1/2} + C₃x^{1/3} + O(x^{50/199+ε})$, where C₁, C₂ and C₃ are constants given on page 261 of [2]. Note that 50/199=0.25125..., thus improving our previous exponent 40/159=0.25157... obtained in [2]. To prove Theorem 1, we shall proceed along the line of approach presented in [2]. The new tool here is an improved version of a result about enumerating certain lattice points due to E. Fouvry and H. Iwaniec (Proposition 2 of [1], which was listed as Lemma 6 in [2]).
8
Content available remote

The number of cube-full numbers in an interval

100%
Liu H.-Q.
Acta Arithmetica
|
1994
|
tom 67
|
nr 1
1-12
9
Content available remote

Numbers with a large prime factor

64%
Liu H.-Q., Wu J.
Acta Arithmetica
|
1999
|
tom 89
|
nr 2
163-187
10
Content available remote

On the number of abelian groups of a given order

32%
Liu H.-Q.
Acta Arithmetica
|
1991
|
tom 59
|
nr 3
261-277
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