Qing Lu

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math.NT2026

Fractional parts of powers of negative rationals

Qing Lu, Weizhe Zheng

We prove that for any real number $I^¾ \neq = 0$ and any coprime integers $p > q \geq 1$ such that $I^¾$ is irrational or $q > 1$ , the image in $R / Z$ of the sequence $(Î¾(-p/…

math.NT2026

Alternating geometric progressions modulo one and Sturmian words

Qing Lu, Weizhe Zheng

Let $b \geq 2$ be an integer. Using Sturmian words we describe all irrational real numbers $I^¾$ such that the image in $R / Z$ of the sequence $(I^¾ (- b)^{n})_{n \geq 0}$ i…