Khai-Hoan Nguyen-Dang

activity

20242026

collaborators

18 papers

math.AG2026

Torsion, Betti rank, and small points in semiabelian schemes

Khai-Hoan Nguyen-Dang

Let $G \to S$ be a semiabelian scheme over a smooth complex algebraic base, with abelian relative dimension $g$ and toric rank $r$ . We prove that a dominating irreducible s…

math.CO2026

Chern flow and Chern moment algebras

Khai-Hoan Nguyen-Dang, Zhenpeng Wang

We construct realizable-volume models over every field for the factorial normalizations of homogeneous Lascoux, Lascoux-atom, and positive Grothendieck packets, including their min…

math.NT2026

Ribet Points, geometric divisibility sequence and order of reductions on semiabelian varieties

Khai-Hoan Nguyen-Dang

Silverman conjectured that the geometric divisibility sequence attached to a Zariski-dense point on an irreducible commutative algebraic group of dimension at least two, with no un…

math.NT2026

Rigid analytic 1-motives and conjugate uniformization of abeloid varieties

Khai-Hoan Nguyen-Dang, Xu Shen, Heer Zhao

Let $K$ be a $p$ -adic field. We study the arithmetic theory of abeloid varieties over $K$ . Our aims are twofold. First, we study the theory of rigid analytic 1-motives, which will…

math.CO2026

Richardson volume models for skew Schur and skew Schur $P / Q$ -functions

Khai-Hoan Nguyen-Dang, with an Appendix by Zhenpeng Wang

We identify ordinary skew Schur polynomials and skew Schur $P$ -functions as top-degree total-Chern intersection polynomials on Richardson varieties in ordinary and Lagrangian Grass…

math.NT2026

Counterexamples of Friedlander--Iwaniec dual sums conjecture

Khai-Hoan Nguyen-Dang

Let $a (n)$ and $b (n)$ be arithmetic sequences, and $A (s) = n \geq 1 \sum a (n) n^{- s}, B (s) = n \geq 1 \sum b (n) n^{- s},$ be the two Dirichlet series related by a certain functional…

math.NT2026

Remarks on a theorem of Silverman

Khai-Hoan Nguyen-Dang, Quang-Khai Nguyen

Motivated by a theorem of Silverman, we consider the following problem. Let $A$ be an abelian variety over a global field $K$ . Given a non-torsion point $P \in A (K)$ , for a suffici…

math.MG2026

Impossibility of a nontrivial Brunn--Minkowski inequality for higher Dirichlet eigenvalue

Trí Minh Lê, Khai-Hoan Nguyen-Dang

Let $λ_{j} (K)$ be the $j$ th Dirichlet eigenvalue of a convex body $K$ . It is well known that $λ_{1}$ satisfies a Brunn--Minkowski inequality: $K \mapsto λ_{1} (K)^{- 1/2}$ is concave on th…

math.NT2026

Minkowski shapes of pure number fields

Khai-Hoan Nguyen-Dang

We study the Minkowski shape of pure number fields \[ K_a=\mathbb Q(θ),\qquad θ^n=a. \] For admissible parameters satisfying an explicit local hypothesis at the primes dividing $n$ …

math.NT2026

On the sequence $gcd (a^{n} - 1, b^{n} - 1)$

Khai-Hoan Nguyen-Dang

For integers $a, b \geq 2$ , put \[ g_n:=\gcd(a^n-1,b^n-1)\qquad(n\ge 1). \] We prove that $(g_{n})$ satisfies a constant-coefficient linear recurrence if and only if $a$ and $b$ are mul…

math.NT2026

Legendre compressions and an integrality conjecture for the Hörmander--Bernhardsson extremal function

Khai-Hoan Nguyen-Dang

We prove Conjecture~2 of Bondarenko, Ortega-Cerdà, Radchenko, and Seip for the three-term recurrence attached to the Hörmander--Bernhardsson extremal function $φ$ . More precisely,…

math.CV2026

Admissibility of Hörmander--Bernhardsson extremal zeros

Khai-Hoan Nguyen-Dang

Let $φ$ be the Hörmander--Bernhardsson extremal function, and let $(\pm τ_{n})_{n \geq 1}$ be its real zeros. Using the recent analytic description of the zero set $τ_{n}$ , we prove that…

math.NT2026

Eisenstein-prime Obstruction Sieve for Monogenicity

Khai-Hoan Nguyen-Dang

Alpöge--Bhargava--Shnidman showed that even a strengthened \emph{no local obstruction} condition for monogenicity does not force a global power integral basis: in the full spaces o…

math.MG2025

Computing intrinsic volumes of sublevel sets and applications

Trí Minh Lê, Khai-Hoan Nguyen-Dang

Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representati…

math.NT2025

$α$ -monogeneity of pure number fields: criterion and density

Khai-Hoan Nguyen-Dang, Nguyen Thai Hung

Let $n \geq 2$ , let $m \in Z ∖ {0}$ , and let $K = Q (α)$ , where $α^{n} = m$ and $X^{n} - m$ is irreducible over $Q$ . We study when the natural order $Z [α]$ …

math.NT2025

The minimal periodicity for integral bases of pure number fields

Khai-Hoan Nguyen-Dang

Fix $n \geq 3$ . For the pure field $K_{a} = Q (θ)$ with $θ^{n} = a$ , where $a \neq = \pm 1$ is $n$ th-power-free, $x^{n} - a$ is irreducible over $Q$ , and Hypothesis~\textup{(\textbf{H})} hol…

math.CO2025

Supersymmetric Schur polynomials have saturated Newton polytopes

Dang Tuan Hiep, Khai-Hoan Nguyen-Dang

We prove that every supersymmetric Schur polynomial has a saturated Newton polytope (SNP). Our approach begins with a tableau-theoretic description of the support, which we encode…

math.NT2024

Kummer-Artin-Schreier-Witt Theory

Huy Dang, Khai-Hoan Nguyen-Dang

We study the problem of lifting the Artin--Schreier--Witt isogeny from characteristic $p > 0$ to characteristic $0$ , which is central to the lifting problem for Galois covers of alge…

Torsion, Betti rank, and small points in semiabelian schemes

Chern flow and Chern moment algebras

Ribet Points, geometric divisibility sequence and order of reductions on semiabelian varieties

Rigid analytic 1-motives and conjugate uniformization of abeloid varieties

Richardson volume models for skew Schur and skew Schur P/Q-functions

Counterexamples of Friedlander--Iwaniec dual sums conjecture

Remarks on a theorem of Silverman

Impossibility of a nontrivial Brunn--Minkowski inequality for higher Dirichlet eigenvalue

Minkowski shapes of pure number fields

On the sequence gcd(an−1,bn−1)

Legendre compressions and an integrality conjecture for the Hörmander--Bernhardsson extremal function

Admissibility of Hörmander--Bernhardsson extremal zeros

Eisenstein-prime Obstruction Sieve for Monogenicity

Computing intrinsic volumes of sublevel sets and applications

α-monogeneity of pure number fields: criterion and density

The minimal periodicity for integral bases of pure number fields

Supersymmetric Schur polynomials have saturated Newton polytopes

Kummer-Artin-Schreier-Witt Theory

Richardson volume models for skew Schur and skew Schur $P / Q$ -functions

On the sequence $gcd (a^{n} - 1, b^{n} - 1)$

$α$ -monogeneity of pure number fields: criterion and density