On general sums involving the floor function with applications to $k$-free numbers

Zhang, Wei

doi:10.48550/arxiv.2112.06156

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2022

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Cited by 1 publication

(2 citation statements)

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“…Regarding our second main result, very recently, Zhang [22] improved the results of Bordellés (1.1), Stuctky [16] and Liu et al [12] by proving using the exponent pair method, that…”

Section: 3)supporting

confidence: 56%

See 1 more Smart Citation

DISTRIBUTION OF r-FREE INTEGERS OVER A FLOOR FUNCTION SET

Tangsupphathawat¹,

Srichan

Laohakosol³

2022

Bull. Aust. Math. Soc.

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For a positive integer $r\geq 2$ , a natural number n is r-free if there is no prime p such that $p^r\mid n$ . Asymptotic formulae for the distribution of r-free integers in the floor function set $S(x):=\{\lfloor x/ n \rfloor :1\leq n\leq x\}$ are derived. The first formula uses an estimate for elements of $S(x)$ belonging to arithmetic progressions. The other, more refined, formula makes use of an exponent pair and the Riemann hypothesis.

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“…Regarding our second main result, very recently, Zhang [22] improved the results of Bordellés (1.1), Stuctky [16] and Liu et al [12] by proving using the exponent pair method, that…”

Section: 3)supporting

confidence: 56%

“…We use the same idea as in [22] to give another formula, which, in the case r = 2, is slightly weaker than that in Theorem 1.3.…”

Section: 3)mentioning

confidence: 99%