Zhao Shen

collaborators

5 papers

math.NT2026

Powers of the Thue--Morse Series: 2-Adic Valuations and Automatic Odd Parts

Zhao Shen

Let $T (x) = \prod_{j \geq 0} (1 - x^{2^{j}}) = \sum_{n \geq 0} t (n) x^{n}$ be the Thue--Morse generating function, and write $T (x)^{m} = \sum_{n \geq 0} t_{m} (n) x^{n}$ for a positive integer $m$ . For a nonzer…

math.CA2026

Intersections and Minkowski Sums of Four-Corner Cantor Dusts with the Unit Circle

Jiangtao Li, Zhao Shen, Yufeng Wu

For $0 < λ < 1/2$ , let $K_{λ}$ be the attractor of the iterated function system ${λ x, λ x + 1 - λ}$ , and put $C_{λ} = K_{λ} \times K_{λ}$ . We study the intersection \[ E_λ=C_λ\cap S^1 \] and the Min…

math.NT2026

Reducing Every Set of 36 Consecutive Integers to Zero by Differences of Squares

Zhao Shen, Youran Wu

For a finite multiset of integers, repeatedly choose two entries $a, b$ and replace them with $∣ a^{2} - b^{2} ∣$ . Hickerson and Kleber asked whether, for every integer $n$ , the set ${n…

math.CO2026

2-adic Valuations of Coefficients of the Fifth and Ninth Powers of the Thue--Morse Generating Function

Zhao Shen, Xinping Wang

Let $T (x) = \prod_{k = 0}^{\infty} (1 - x^{2^{k}})$ be the generating function of the Thue--Morse sequence, and write $T (x)^{m} = \sum_{n \geq 0} t_{m} (n) x^{n}$ . We prove exact formulas for the $2$ -a…

math.CO2026

Unboundedness of the Coefficients of Higher Powers of a Unimodular Power Series

Zhao Shen

Let $R (z) = \sum_{n = 0}^{\infty} r_{n} z^{n}$ be a power series with $∣ r_{n} ∣ = 1$ for every $n \geq 0$ . We show that for each integer $m \geq 2$ , the coefficient sequence of $R (z)^{m}$ is unbounde…