Shengtong Zhang

activity

20192026

most citedEquiangular lines with a fixed angle

65 citations · 89 across the 16 of their papers we have counts for

collaborators

16 papers

math.NT2026

Maximising the number of solutions to linear equations

Žarko Ranđelović, Xuancheng Shao, Max Wenqiang Xu +2

We study the asymptotically maximal possible number of integer solutions to the linear equation $a x + b y + cz = 0$ with a fixed choice of $a, b, c \in Z$ and variables $x, y,…

cs.AI2026

The Problem Is the Problem: Towards Scalable Mathematical Discovery

Zeyu Zheng, Shengtong Zhang, Jeremy Avigad +2

AI systems are increasingly capable of contributing to mathematical research. In research practice, frontier-model reasoning is a limited resource, and expert mathematical review i…

math.CO2023★ 2 cited

Hypergraph independence polynomials with a zero close to the origin

Shengtong Zhang

For each uniformity $k \geq 3$ , we construct $k$ -uniform linear hypergraphs $G$ with arbitrarily large maximum degree $Δ$ whose independence polynomial $Z_{G}$ has a root $λ$ with $\…

math.CO2023

A Short Proof to Defant and Kravitz's theorem on the Length of Hitomezashi Loops

Qiuyu Ren, Shengtong Zhang

We provide a shorter proof to Defant and Kravitz's theorem (arXiv:2201.03461, Theorem 1.2) on the length of Hitomezashi loops modulo 8.

math.NT2022

Euler-Kronecker constants for cyclotomic fields

Letong Hong, Ken Ono, Shengtong Zhang

The Euler-Mascheroni constant $γ = 0.5772 \dots$ is the $K = Q$ example of an Euler-Kronecker constant $γ_{K}$ of a number field $K .$ In this note we consider the size of the $…

math.CO2022

Log-Concavity in Powers of Infinite Series Close to $(1 - z)^{- 1}$

Shengtong Zhang

In this paper, we use the analytic method of Odlyzko and Richmond to study the log-concavity of power series. If $f (z) = \sum_{n} a_{n} z^{n}$ is an infinite series with $a_{n} \geq 1$ and…

math.CO2021

Domination polynomial is unimodal for large graphs with a universal vertex

Shengtong Zhang

For a undirected simple graph $G$ , let $d_{i} (G)$ be the number of $i$ -element dominating vertex set of $G$ . The domination polynomial of the graph $G$ is defined as $$D(G, x) = \sum…

math.CO2021

Note on the Turán number of the $3$ -linear hypergraph $C_{13}$

Chaoliang Tang, Hehui Wu, Shengtong Zhang +1

Let the crown $C_{13}$ be the linear $3$ -graph on $9$ vertices ${a, b, c, d, e, f, g, h, i}$ with edges $E = {{a, b, c}, {a, d, e}, {b, f, g}, {c, h, i}} .$ Proving a conjecture o…

math.CO2021

Graphs with high second eigenvalue multiplicity

Milan Haiman, Carl Schildkraut, Shengtong Zhang +1

Jiang, Tidor, Yao, Zhang, and Zhao recently showed that connected bounded degree graphs have sublinear second eigenvalue multiplicity (always referring to the adjacency matrix). Th…

math.NT2021★ 1 cited

Proof of the elliptic expansion Moonshine Conjecture of Căldăraru, He, and Huang

Letong Hong, Michael H. Mertens, Ken Ono +1

Using predictions in mirror symmetry, Căldăraru, He, and Huang recently formulated a "Moonshine Conjecture at Landau-Ginzburg points" for Klein's modular $j$ -function at $j = 0$ and…

math.CO2021★ 3 cited

No extremal square-free words over large alphabets

Letong Hong, Shengtong Zhang

A word is square-free if it does not contain any square (a word of the form $X X$ ), and is extremal square-free if it cannot be extended to a new square-free word by inserting a sin…

math.NT2021★ 2 cited

Proof of the Ballantine-Merca Conjecture and theta function identities modulo 2

Letong Hong, Shengtong Zhang

For positive integers $m$ we consider the theta functions $f_{m} (z) := \sum_{mk + 1 square} q^{k}$ . Due to classical identities of Jacobi, it is known that $$f_4\equiv f_6f_{12}\pmo…

math.CO2020★ 6 cited

Towards Heim and Neuhauser's Unimodality Conjecture on the Nekrasov-Okounkov polynomials

Letong Hong, Shengtong Zhang

Let $Q_{n} (z)$ be the polynomials associated with the Nekrasov-Okounkov formula $n \geq 1 \sum Q_{n} (z) q^{n} := m = 1 \prod \infty (1 - q^{m})^{- z - 1} .$ In this paper we partially a…

math.NT2020★ 1 cited

A Bombieri-Vinogradov Theorem for primes in short intervals and small sectors

Tanmay Khale, Cooper O'Kuhn, Apoorva Panidapu +2

Let $K$ be a finite Galois extension of $Q$ . We count primes in short intervals represented by the norm of a prime ideal of $K$ satisfying a small sector condition determi…

math.CO2020★ 9 cited

Spherical two-distance sets and eigenvalues of signed graphs

Zilin Jiang, Jonathan Tidor, Yuan Yao +2

We study the problem of determining the maximum size of a spherical two-distance set with two fixed angles (one acute and one obtuse) in high dimensions. Let $N_{α, β} (d)$ denote th…

math.CO2019★ 65 cited

Equiangular lines with a fixed angle

Zilin Jiang, Jonathan Tidor, Yuan Yao +2

Solving a longstanding problem on equiangular lines, we determine, for each given fixed angle and in all sufficiently large dimensions, the maximum number of lines pairwise separat…

Maximising the number of solutions to linear equations

The Problem Is the Problem: Towards Scalable Mathematical Discovery

Hypergraph independence polynomials with a zero close to the origin

A Short Proof to Defant and Kravitz's theorem on the Length of Hitomezashi Loops

Euler-Kronecker constants for cyclotomic fields

Log-Concavity in Powers of Infinite Series Close to (1−z)−1

Domination polynomial is unimodal for large graphs with a universal vertex

Note on the Turán number of the 3-linear hypergraph C13​

Graphs with high second eigenvalue multiplicity

Proof of the elliptic expansion Moonshine Conjecture of Căldăraru, He, and Huang

No extremal square-free words over large alphabets

Proof of the Ballantine-Merca Conjecture and theta function identities modulo 2

Towards Heim and Neuhauser's Unimodality Conjecture on the Nekrasov-Okounkov polynomials

A Bombieri-Vinogradov Theorem for primes in short intervals and small sectors

Spherical two-distance sets and eigenvalues of signed graphs

Equiangular lines with a fixed angle

Log-Concavity in Powers of Infinite Series Close to $(1 - z)^{- 1}$

Note on the Turán number of the $3$ -linear hypergraph $C_{13}$