K. Nguyen

activity

20072023

most citedA Tight Lower Bound to the Outage Probability of Discrete-Input Block-Fading Channels

25 citations · 112 across the 26 of their papers we have counts for

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math.NT2021

Transcendence of polynomial canonical heights

Khoa D. Nguyen

There are two fundamental problems motivated by Silverman's conversations over the years concerning the nature of the exact values of canonical heights of $f(z)\in\bar{\mathbb{Q}}(…

math.NT2021

Endomorphisms of positive characteristic tori: entropy and zeta function

Keira Gunn, Khoa D. Nguyen, J. C. Saunders

Let $F$ be a finite field of order $q$ and characteristic $p$ . Let $Z_{F} = F [t]$ , $Q_{F} = F (t)$ , $R_{F} = F ((1/ t))$ equipped with the discrete valuation for which…

math.NT2021

N-colored generalized Frobenius partitions: Generalized Kolitsch identities

Zafer Selcuk Aygin, Khoa D. Nguyen

Let $N \geq 1$ be squarefree with $(N, 6) = 1$ . Let $c ϕ_{N} (n)$ denote the number of $N$ -colored generalized Frobenius partition of $n$ introduced by Andrews in 1984. We prove $$ cϕ_N(n)…

math.NT2020

Transcendental Series of Reciprocals of Fibonacci and Lucas Numbers

Khoa D. Nguyen

Let $F_{1} = 1, F_{2} = 1, \dots$ be the Fibonacci sequence. Motivated by the identity $k = 0 \sum \infty \frac{1}{F _{2^{k}}} = \frac{7 - 5}{2}$ , Erdös and Graham asked wheth…

math.NT2020

Monogenic pure cubics

Zafer Selcuk Aygin, Khoa D. Nguyen

Let $k \geq 2$ be a square-free integer. We prove that the number of square-free integers $m \in [1, N]$ such that $(k, m) = 1$ and $Q (3 k^{2} m)$ is monogenic is $\gg N^{1…

math.NT2019

An analogue of Ruzsa's conjecture for polynomials over finite fields

Jason P. Bell, Khoa D. Nguyen

In 1971, Ruzsa conjectured that if $f : N \to Z$ with $f (n + k) \equiv f (n)$ mod $k$ for every $n, k \in N$ and $f (n) = O (θ^{n})$ with $θ < e$ then $f$ is a po…