D. Q. Nguyen

activity

20122021

most citedThe classical umbral calculus, and the flow of a Drinfeld module

3 citations · 8 across the 12 of their papers we have counts for

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13 papers · 1 filter

math.NT2020

On the generating polynomials for the distribution of generalized binomial coefficients in discrete valuation domains

Dong Quan Ngoc Nguyen

For a discrete valuation domain $V$ with maximal ideal $m$ such that the residue field $V / m$ is finite, there exists a sequence of polynomials $(F_n(x))_{n \g…

math.NT2020★ 2 cited

Effectively bounded idempotent generation of certain $2 \times 2$ singular matrices by idempotent matrices over real quadratic number rings

Dong Quan Ngoc Nguyen

Let $k = Q (α)$ be a real quadratic number field, where $α$ is a positive square-free integer. Let $O_{k}$ be the ring of integers of $k$ . In this paper, we pr…

math.NT2018

Polynomial Parametrization for $SL_{2}$ over Quadratic Number Rings

Michael Larsen, Dong Quan Ngoc Nguyen

If $R$ is the ring of integers of a number field, then there exists a polynomial parametrization of the set $SL_{2} (R)$ , i.e., an element $A \in \text{SL}_2(\mathbb{Z}[x_1,\ld…

math.NT2017

Waring's problem for unipotent algebraic groups

Michael Larsen, Dong Quan Ngoc Nguyen

In this paper, we formulate an analogue of Waring's problem for an algebraic group $G$ . At the field level we consider a morphism of varieties $f : A^{1} \to G$ and ask w…

math.NT2016

The distribution of the Carlitz binomial coefficients modulo a prime

Dong Quan Ngoc Nguyen

For a nonnegative integer $n$ , and a prime $℘$ in $F_{q} [T]$ , we prove a result that provides a method for computing the number of integers $m$ with $0 \leq m \leq n$ for wh…

math.NT2015

Representation of units in cyclotomic function fields

Dong Quan Ngoc Nguyen

Hilbert's Satz 90 tells us that for a given cyclic extension $K / k$ , a unit of norm $1$ in $K$ can be written as a quotient of conjugate elements in $K$ . For the extensions $\mathbb…

math.NT2015

Certain sets over function fields are polynomial families

Dong Quan Ngoc Nguyen

In 1938, Skolem conjectured that $SL_{n} (Z)$ is not a polynomial family for any $n \geq 2$ . Carter and Keller disproved Skolem's conjecture for all $n \geq 3$ by prov…

math.NT2015

Function field analogues of Bang-Zsigmondy's theorem and Feit's theorem

Dong Quan Ngoc Nguyen

In the number field context, Bang-Zsigmondy's theorem states that for any integers $u, m > 1$ , there exists a prime divisor $p$ of $u^{m} - 1$ such that $p$ does not divide $u^{n} - 1$ …

math.NT2014★ 2 cited

Algebraic families of hyperelliptic curves violating the Hasse principle

Dong Quan Ngoc Nguyen

In $2000$ , Colliot-Thélène and Poonen showed how to construct algebraic families of genus one curves violating the Hasse principle. Poonen explicitly constructed an algebraic famil…

math.NT2014

Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields

Dong Quan Ngoc Nguyen

In this paper, we introduce a Carlitz module analogue of Mersenne primes, and prove Carlitz module analogues of several classical results concerning Mersenne primes. In contrast to…

math.NT2014

A Carlitz module analogue of the Grunwald--Wang theorem

Dong Quan Ngoc Nguyen

The classical Grunwald--Wang theorem is an example of a local--global (or Hasse) principle stating that except in some special cases which are precisely determined, an element $m$ …

math.NT2014★ 3 cited

The classical umbral calculus, and the flow of a Drinfeld module

Dong Quan Ngoc Nguyen

David Goss developed a very general Fourier transform in additive harmonic analysis in the function field setting. In order to introduce the Fourier transform for continuous charac…

math.NT2012★ 1 cited

Generalized Mordell curves, generalized Fermat curves, and the Hasse principle

Dong Quan Ngoc Nguyen

A generalized Mordell curve of degree $n \geq 3$ over $\bQ$ is the smooth projective model of the affine curve of the form $A z^{2} = B x^{n} + C$ , where $A, B, C$ are nonzero integers. A…

On the generating polynomials for the distribution of generalized binomial coefficients in discrete valuation domains

Effectively bounded idempotent generation of certain 2×2 singular matrices by idempotent matrices over real quadratic number rings

Polynomial Parametrization for SL2​ over Quadratic Number Rings

Waring's problem for unipotent algebraic groups

The distribution of the Carlitz binomial coefficients modulo a prime

Representation of units in cyclotomic function fields

Certain sets over function fields are polynomial families

Function field analogues of Bang-Zsigmondy's theorem and Feit's theorem

Algebraic families of hyperelliptic curves violating the Hasse principle

Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields

A Carlitz module analogue of the Grunwald--Wang theorem

The classical umbral calculus, and the flow of a Drinfeld module

Generalized Mordell curves, generalized Fermat curves, and the Hasse principle

Effectively bounded idempotent generation of certain $2 \times 2$ singular matrices by idempotent matrices over real quadratic number rings

Polynomial Parametrization for $SL_{2}$ over Quadratic Number Rings