C. Yip

activity

20232026

most citedImproved upper bounds on Diophantine tuples with the property

D (n)

2 citations · 6 across the 11 of their papers we have counts for

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5 papers · 1 filter

math.NT2024

Upper Bounds on Polynomial Root Separation

Greg Knapp, Chi Hoi Yip

In this paper, we consider the relationship between the Mahler measure of a polynomial and its separation. In 1964, Mahler proved that if $f (x) \in Z [x]$ is separable of d…

math.NT2024

On the fractional parts of certain sequences of $ξ α^{n}$

Xiang Gao, Chi Hoi Yip

Assume that $α > 1$ is an algebraic number and $ξ \neq = 0$ is a real number. We are concerned with the distribution of the fractional parts of the sequence $(ξ α^{n})$ . Under various Dio…

math.NT2024★ 1 cited

A strengthening of McConnel's theorem on permutations over finite fields

Chi Hoi Yip

Let $p$ be a prime, $q = p^{n}$ , and $D \subset F_{q}^{*}$ . A celebrated result of McConnel states that if $D$ is a proper subgroup of $F_{q}^{*}$ , and $f:\mathbb{F}_q \to \m…

math.NT2024★ 2 cited

Improved upper bounds on Diophantine tuples with the property $D (n)$

Chi Hoi Yip

Let $n$ be a non-zero integer. A set $S$ of positive integers is a Diophantine tuple with the property $D (n)$ if $ab + n$ is a perfect square for each $a, b \in S$ with $a \neq = b$ . It…

math.NT2023★ 2 cited

Restricted sumsets in multiplicative subgroups

Chi Hoi Yip

We establish the restricted sumset analogue of the celebrated conjecture of Sárközy on additive decompositions of the set of nonzero squares over a finite field. More precisely, we…

Upper Bounds on Polynomial Root Separation

On the fractional parts of certain sequences of ξαn

A strengthening of McConnel's theorem on permutations over finite fields

Improved upper bounds on Diophantine tuples with the property D(n)

Restricted sumsets in multiplicative subgroups

On the fractional parts of certain sequences of $ξ α^{n}$

Improved upper bounds on Diophantine tuples with the property $D (n)$