Kui Liu

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math.NT2023

On the distribution of $k$ -free numbers on the view point of random walks

Kui Liu, Meijie Lu

In this paper, we investigate the distribution of $k$ -free numbers in a class of $α$ -random walks on the integer lattice $Z$ . In these walks, the walker starts from a non-…

math.NT2016

Cancellations between Kloosterman sums modulo a prime power with prime arguments

Kui Liu, Igor E. Shparlinski, Tianping Zhang

We obtain a nontrivial bound for cancellations between the Kloosterman sums modulo a large prime power with a prime argument running over very short interval, which in turn is base…

math.NT2016

Bilinear Forms with Exponential Sums with Binomials

Kui Liu, Igor E. Shparlinski, Tianping Zhang

We obtain several estimates for bilinear form with exponential sums with binomials $m x^{k} + n x^{ℓ}$ . In particular we show the existence of nontrivial cancellations between such su…

math.NT2016

Squares in Piatetski--Shapiro Sequences

Kui Liu, Igor E. Shparlinski, Tianping Zhang

We study the distribution of squares in a Piatetski-Shapiro sequence $(⌊ n^{c} ⌋)_{n \in N}$ with $c > 1$ and $c \neq \in N$ . We also study more genera…

On the distribution of k-free numbers on the view point of random walks

Cancellations between Kloosterman sums modulo a prime power with prime arguments

Bilinear Forms with Exponential Sums with Binomials

Squares in Piatetski--Shapiro Sequences

On the distribution of $k$ -free numbers on the view point of random walks