Khang Tran

activity

20092026

most citedConnections between discriminants and the root distribution of polynomials with rational generating function

25 citations · 73 across the 15 of their papers we have counts for

collaborators

19 papers

math.CV2026

On zero distribution of the sum of Gegenbauer polynomials

Khang Tran, Riley White

We study the zero distribution of the sum of the first $n$ Gegenbauer polynomials \[ S_n^{(α)}(z)=\sum_{k=0}^n C_{k}^{(α)}(z). \] We prove that for $α > 1$ , the zeros of $S_n^{(α)}(z…

math.NT2023

Zeros of Taylor polynomials formed by a three-term recurrence

Juhoon Chung, Khang Tran

From a sequence ${a_{n}}_{n = 0}^{\infty}$ of real numbers satisfying a three-term recurrence, we form a sequence of polynomials $\left\{ P_{m}(z)\right\} _{m=0}^{\inf…

math.CV2023

On the zeros of certain Sheffer sequences and their cognate sequences

Gi-Sang Cheon, Tamás Forgács, Khang Tran

Given a Sheffer sequence of polynomials, we introduce the notion of an associated sequence called the cognate sequence. We study the relationship between the zeros of this pair of…

math.CO2022

The zero locus and some combinatorial properties of certain exponential Sheffer sequences

Gi-Sang Cheon, Tamás Forgács, Arnauld Mesinga Mwafise +1

We present combinatorial and analytical results concerning a Sheffer sequence with an exponential generating function of the form $G (s, z) = e^{cz s + α z^{2} + β z^{4}}$ , where $α, β, c \in…

math.CO2021

On combinatorial properties and the zero distribution of certain Sheffer sequences

Gi-Sang Cheon, Tamás Forgács, Hana Kim +1

We present combinatorial and analytical results concerning a Sheffer sequence with a generating function of the form $G (x, z) = Q (z)^{x} Q (- z)^{1 - x}$ , where $Q$ is a quadratic polynomi…

math.CV2020

Zeros of a table of polynomials satisfying a four-term contiguous relation

Jack Luong, Khang Tran

For any $A (z), B (z), C (z) \in C [z]$ , we study the zero distribution of a table of polynomials ${P_{m, n} (z)}_{m, n \in N_{0}}$ satisfying the recurrence re…

math.CA2020

Zeros of a binomial combination of Chebyshev polynomials

Summer Al Hamdani, Khang Tran

For $0 < α < 1$ , we study the zeros of the sequence of polynomials ${P_{m} (z)}_{m = 0}^{\infty}$ generated by the reciprocal of $(1 - t)^{α} (1 - 2 z t + t^{2})$ , expanded as a power…

math.CV2019

Linear combinations of polynomials with three-term recurrence

Khang Tran, Maverick Zhang

We study the zero distribution of the sum of the first $n$ polynomials satisfying a three-term recurrence whose coefficients are linear polynomials. We also extend this sum to a li…

math.CV2018

Hyperbolic polynomials and linear-type generating functions

Tamás Forgács, Khang Tran

We prove that the polynomials generated by the relation $m = 0 \sum \infty H_{m} (z) t^{m} = \frac{1}{P ( t ) + z t ^{r} Q ( t )}$ are hyperbolic for $m ≫ 1$ given that the zeros o…

math.CV2018

Zeros of polynomials with four-term recurrence and linear coefficients

Khang Tran, Andres Zumba

This paper investigates the zero distribution of a sequence of polynomials ${P_{m} (z)}_{m = 0}^{\infty}$ generated by the reciprocal of $1 + c t + B (z) t^{2} + A (z) t^{3}$ wher…

math.CV2017★ 12 cited

Zeros of polynomials with four-term recurrence

Khang Tran, Andres Zumba

For any real numbers $b, c \in R$ , we form the sequence of polynomials ${H_{m} (z)}_{m = 0}^{\infty}$ satisfying the four-term recurrence \[ H_{m}(z)+cH_{m-1}(z)+…

math.CV2016

On the zeros of polynomials generated by rational functions with a hyperbolic polynomial type denominator

Tamás Forgács, Khang Tran

This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a denominator of the form $G (z, t) = P (t) + z t^{r}$ , where the zeros…

math.CV2016★ 19 cited

The root distribution of polynomials with a three-term recurrence

Khang Tran

For any fixed positive integer $n$ , we study the root distribution of a sequence of polynomials $H_{m} (z)$ satisfying the rational generating function \[ \sum_{m=0}^{\infty}H_{m}(z…

math.CV2016★ 25 cited

Connections between discriminants and the root distribution of polynomials with rational generating function

Khang Tran

Let $H_{m} (z)$ be a sequence of polynomials whose generating function $\sum_{m = 0}^{\infty} H_{m} (z) t^{m}$ is the reciprocal of a bivariate polynomial $D (t, z)$ . We show that in the t…

math.CV2016★ 1 cited

Pair correlation of roots of rational functions with rational generating functions and quadratic denominators

Khang Tran, Alexandru Zaharescu

For any rational functions with complex coefficients $A (z), B (z)$ and $C (z)$ , where $A (z)$ , $C (z)$ are not identically zero, we consider the sequence of rational functions $H_{m}(z…

math.CV2016★ 5 cited

Discriminants of Polynomials Related to Chebyshev Polynomials: The 'Mutt and Jeff' Syndrome

Khang Tran

The discriminants of certain polynomials related to Chebyshev polynomials factor into the product of two polynomials, one of which has coefficients that are much larger than the ot…

math.CV2016★ 2 cited

Discriminants of Chebyshev-like polynomials and their generating functions

Khang Tran

In his paper of 2000, Kenneth B. Stolarsky made various observations and conjectures about discriminants and generating functions of certain types of Chebyshev-like polynomials. We…

math.CV2016★ 9 cited

Polynomials with rational generating functions and real zeros

Tamas Forgacs, Khang Tran

This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a binomial-type denominator. We show that every member of a two…

cs.SC2009

Generating functions of Chebyshev-like polynomials

Alin Bostan, Bruno Salvy, Khang Tran

In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like pol…