Quanyu Tang

most citedPrimitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond

1 citations · 2 across the 12 of their papers we have counts for

collaborators

13 papers

math.SP2026

Neumann--Dirichlet eigenvalue comparison at the first Dirichlet threshold in the plane

Quanyu Tang, Haiqi Zhang

Let $Ω \subset R^{2}$ be a bounded connected Lipschitz domain, and let ${μ_{j} (Ω)}_{j \geq 1}$ and ${λ_{j} (Ω)}_{j \geq 1}$ denote the Neumann and Dirichlet Laplacian eigenvalues, r…

math.CV2026

Three omitted values and non-Blaschke point divisors in half-planes

Quanyu Tang, Bokai Cui, Wei He +4

We construct a real meromorphic function $F$ on $C$ such that $F^{- 1} ({0, 1, \infty}) \subset R$ , while $F$ is not of bounded type in either half-plane. More strongly…

math.CO2026

Supersaturation in Nosal graphs: Triangles and books

Hongzhang Chen, Yongtao Li, Quanyu Tang

In this paper, we use the spectral surplus $λ (G) - m$ to measure how far $G$ lies above the Nosal threshold, and prove the following edge-spectral supersaturation results fo…

math.AP2026

Sharp ratios for low-index Neumann eigenvalues on convex domains

Quanyu Tang, Haiqi Zhang

Let $Ω \subset R^{N}$ be a bounded open convex set, and let $0 = μ_{0} (Ω) < μ_{1} (Ω) \leq μ_{2} (Ω) \leq \dots$ be the Neumann eigenvalues of the Laplacian, repeated according to multiplicit…

math.AP2026

The Ashbaugh--Benguria reciprocal-gap conjecture for Dirichlet eigenvalues

Yanyang Li, Quanyu Tang, Haiqi Zhang

We prove the Ashbaugh--Benguria reciprocal-gap conjecture for the Dirichlet Laplacian in every dimension $N \geq 2$ . Specifically, if $Ω \subset R^{N}$ is a bounded domain and $$…

math.CO2026

Path-Minimality of $p$ -Energy for Connected Graphs

Yinchen Liu, Quanyu Tang

Let $G$ be a simple connected graph on $n$ vertices, and let $λ_{1} (G), λ_{2} (G), \dots, λ_{n} (G)$ be the eigenvalues of its adjacency matrix $A (G)$ . For $p > 0$ , define the $p$ -energy of $G…

math.AP2026

A sharp fixed-volume product inequality for the first $N$ nonzero Steklov eigenvalues

Haiqi Zhang, Quanyu Tang, Yanyang Li

We prove a sharp fixed-volume product inequality for the first $N$ nonzero Steklov eigenvalues of bounded Lipschitz domains in $R^{N}$ . More precisely, if $N \geq 2$ and $Ω\subs…

math.NT2026

Consecutive integers free of certain prime factors

Wouter van Doorn, Quanyu Tang

Let $n_{k}$ denote the least integer $n > 2 k$ such that $(n - k) (n - k + 1) \dots (n - 1)$ is not divisible by any prime in the interval $(k, 2 k)$ . Confirming a conjecture of Erdős, we prove tha…

math.NT2026

Gaps in Multiplicative Sidon Sets II

Wouter van Doorn, Quanyu Tang

With $ρ = \frac{13 - 69}{10} \approx 0.47$ , it was recently established that there exist multiplicative Sidon sets (sets without any non-trivial solutions to $ab = c d$ ) in $\{1…

math.NT2026

Gaps in Multiplicative Sidon Sets

Wouter van Doorn, Pietro Monticone, Quanyu Tang

For a positive integer $n$ , let $g (n)$ denote the infimum of all real numbers $L$ such that there exists a multiplicative Sidon set $A \subseteq {1, 2, \dots, n}$ that intersects ever…

math.NT2026★ 1 cited

Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond

Boris Alexeev, Kevin Barreto, Yanyang Li +5

A set of integers is primitive if no number in the set divides another. We introduce a new method for bounding Erdős sums of primitive sets, suggested from output of GPT-5.4 Pro, b…

math.FA2025★ 1 cited

Generalizing Lee's conjecture on the sum of absolute values of matrices

Quanyu Tang, Shu Zhang

Let $∥ \cdot ∥_{p}$ denote the Schatten $p$ -norm of matrices and $∥ \cdot ∥_{F}$ the Frobenius norm. For a square matrix $X$ , let $∣ X ∣$ denote its absolute value. In 2010, Eun-…

math.CV2025

Dual Smale's mean value conjecture for odd polynomials

Quanyu Tang

We prove Dual Smale's mean value conjecture for all odd polynomials with nonzero linear term. Precisely, if $P$ is an odd polynomial of degree $d \geq 3$ with $P (0) = 0$ and $P^{'} (0) = 1$ ,…

Neumann--Dirichlet eigenvalue comparison at the first Dirichlet threshold in the plane

Three omitted values and non-Blaschke point divisors in half-planes

Supersaturation in Nosal graphs: Triangles and books

Sharp ratios for low-index Neumann eigenvalues on convex domains

The Ashbaugh--Benguria reciprocal-gap conjecture for Dirichlet eigenvalues

Path-Minimality of p-Energy for Connected Graphs

A sharp fixed-volume product inequality for the first N nonzero Steklov eigenvalues

Consecutive integers free of certain prime factors

Gaps in Multiplicative Sidon Sets II

Gaps in Multiplicative Sidon Sets

Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond

Generalizing Lee's conjecture on the sum of absolute values of matrices

Dual Smale's mean value conjecture for odd polynomials

Path-Minimality of $p$ -Energy for Connected Graphs

A sharp fixed-volume product inequality for the first $N$ nonzero Steklov eigenvalues