Maciej Ulas

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20232026

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math.NT2026

Hankel determinants of weighted binary sums of digits

Bartosz Sobolewski, Maciej Ulas

Let $s_{w}$ be the weighted binary sum-of-digits function associated with an arbitrary sequence of complex weights $w = (w_{j})_{j \geq 0}$ . We investigate Hankel determ…

math.NT2026

There are infinitely many Hilbert cubes of dimension 3 in the set of squares

Andrew Bremner, Christian Elsholtz, Maciej Ulas

For an integer tuple $(a_{0}, a_{1}, \dots, a_{d})$ with $a_{i} \neq = 0$ for $i = 1, \dots, d$ , we define the associated Hilbert cube by \[ H(a_0;a_1,\ldots,a_d) = \left\{ a_0+\sum_{i=1}^d \vareps…