Viêt-Anh Nguyên

activity

20232026

collaborators

10 papers

math.NT2026

Erdős-Moser Equation in Arithmetic Progressions

Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu

We consider the Erdős-Moser equation $1^{k} + 2^{k} + \dots + (m - 1)^{k} = m^{k}$ in arithmetic progressions. We prove among other things that when $k = 2$ , for any solution to exist, the above sum…

math.NT2026

Admissible Pairs: A Variation to Pollock Conjectures

Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu

We introduce a notion of an admissible pair, and prove a variation to Pollock's conjectures on icosahedral and dodecahedral numbers.

math.NT2026

Effective Estimates for a Class of Farey Fraction Sums and Bounds for Mundici-Type Constants

Anji Dong, Huy Xuan Nguyen, Vi Anh Nguyen +1

Let $D_{2} (Q)$ denote the sum of squared distances between consecutive Farey fractions in the full interval $(0, 1]$ . Daniele Mundici conjectured that $C(Q):=D_{2}(Q)\cdot Q^2/\log…

math.NT2026

On a Conjecture about Sums Involving Farey Fractions

Anji Dong, Xinyi Li, Vi Anh Nguyen

In this paper, we prove a conjecture by Daniele Mundici on the sum of squared distances between consecutive elements in the $Q$ -th Farey sequence for $Q \in Z$ and $Q \geq 2$ …

physics.optics2025

Generalized Non-Hermitian Hamiltonian for Guided Resonances in Photonic Crystal Slabs

Viet Anh Nguyen, Hung Son Nguyen, Zhiyi Yuan +6

We develop a generalized non-Hermitian Hamiltonian formalism for guided resonances in photonic crystal slabs, derived directly from Maxwell's equations through a systematic guided-…

math.CV2025

Uniqueness of tangent currents for positive closed currents

Viet-Anh Nguyen, Tuyen Trung Truong

Let $X$ be a complex manifold $X$ of dimension $k,$ and let $V \subset X$ be a Kähler submanifold of dimension $l,$ and let $B \subset V$ be a piecewise $C^{2}$ -smooth domain…

math.CV2025

The generalized Lelong numbers and intersection theory

Viet-Anh Nguyen

Let $X$ be a complex manifold of dimension $k,$ and $(V, ω)$ be a Kähler submanifold of dimension $l$ in $X,$ and $B ⋐ V$ be a domain with $C^{2}$ -smooth boundary. Let…

math.CV2024

Generic singularities of holomorphic foliations by curves on $P^{n}$

Sahil Gehlawat, Viêt-Anh Nguyên

Let $F_{d} (P^{n})$ be the space of all singular holomorphic foliations by curves on $P^{n}$ ( $n \geq 2$ ) with degree $d \geq 1.$ We show that there is subset…

math.CV2024

Zeros of random holomorphic sections of big line bundles with continuous metrics

Turgay Bayraktar, Dan Coman, George Marinescu +1

Let $X$ be a compact normal complex space, $L$ be a big holomorphic line bundle on $X$ and $h$ be a continuous Hermitian metric on $L$ . We consider the spaces of holomorphic sectio…

math.CV2023

Restricted spaces of holomorphic sections vanishing along subvarieties

Dan Coman, George Marinescu, Viêt-Anh Nguyên

Let $X$ be a compact normal complex space of dimension $n$ and $L$ be a holomorphic line bundle on $X$ . Suppose that $Σ = (Σ_{1}, \dots, Σ_{ℓ})$ is an $ℓ$ -tuple of distinct irreduci…

Erdős-Moser Equation in Arithmetic Progressions

Admissible Pairs: A Variation to Pollock Conjectures

Effective Estimates for a Class of Farey Fraction Sums and Bounds for Mundici-Type Constants

On a Conjecture about Sums Involving Farey Fractions

Generalized Non-Hermitian Hamiltonian for Guided Resonances in Photonic Crystal Slabs

Uniqueness of tangent currents for positive closed currents

The generalized Lelong numbers and intersection theory

Generic singularities of holomorphic foliations by curves on Pn

Zeros of random holomorphic sections of big line bundles with continuous metrics

Restricted spaces of holomorphic sections vanishing along subvarieties

Generic singularities of holomorphic foliations by curves on $P^{n}$