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…