Author

Quanyu Tang

View on Semantic Scholar

2 papers indexed here

We haven’t gathered this author’s papers yet. Follow them and we’ll fetch their work.

Not the right person? Other researchers publish under this name.

Preprint Aug 2026

Graph Eigenvalues and Projection Constants

For an integer $k\ge2$, let $\lambda_k(G)$ denote the $k$th largest adjacency eigenvalue of a graph $G$. For every graph $G$ on $n$ vertices and every $2 \leq k \leq n$, we prove \[ \lambda_k(G) \le \frac{(k-2)\sqrt{k+1}+2}{2k(k-1)}\,n-1. \] Our bound is tight for $k\in\{2,3,4,8,24\}$. We obtain it by reducing the graph-eigenvalue problem to an extremal problem for orthogonal projections and then applying the general upper bound on the absolute projection constant $\gamma(r)$ due to Der\k{e}gowska and Lewandowska. We also give an alternative proof of their bound by repairing the Gegenbauer-polynomial argument of K\"onig and Tomczak-Jaegermann. The resulting slack identity yields a strict improvement in every even dimension $r\ge4$ for which $r+2$ is not a perfect square.

Varun Sivashankar, Quanyu Tang, Tanay Wakhare · 0 citations

Preprint Aug 2026

Integral Representations and Asymptotics for a Family of Areal Mahler Measures

We answer a problem posed by Matilde Lal\'in concerning the areal Mahler measures of the multivariable polynomial family $$ P_n(x_1,\ldots,x_n,u) = \prod_{j=1}^n(1+x_j) + u\prod_{j=1}^n(1-x_j), \qquad n\geq1. $$ Using a probabilistic reformulation, we derive convolution and one-dimensional Fourier integral representations for $\mathrm m_{\mathbb D}(P_n)$. These representations yield strict alternating signs for all forward differences of the sequence $\bigl(\mathrm m_{\mathbb D}(P_n)\bigr)_{n\geq1}$, as well as an explicit three-term asymptotic expansion as $n\to\infty$.

Quanyu Tang, Shu Zhang · 0 citations