Ratio of sum of digits functions in two bases

Abstract: In 2019 La Bretèche, Stoll and Tenenbaum showed that the ratio of the sum of digits function $s_p(n)/s_q(n)$ of two multiplicatively independent bases $p$ and $q$ is dense in $\mathbb{Q}^+$. Spiegelhofer proved that when $p = 2$ and $q = 3$, the ratio 1 is attained infinitely many times, which he extended jointly with Drmota to arbitrary values in $\mathbb{Q}^+$. In this talk, I generalize this result further, showing that for two arbitrary multiplicatively independent bases, $s_p(n)/s_q(n)$ attains every value in $\mathbb{Q}^+$ infinitely many times.

dynamical systemsnumber theory

Audience: researchers in the topic

One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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