Shengtong Zhang

activity

20202022

collaborators

5 papers

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.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.NT2021

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

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