P. Allaart

activity

20062023

most citedOn the continuity of the Hausdorff dimension of the univoque set

17 citations · 59 across the 22 of their papers we have counts for

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5 papers · 1 filter

math.NT2021

On the existence of numbers with matching continued fraction and decimal expansions

Pieter Allaart, Stephen Jackson, Taylor Jones +1

A Trott number is a number $x \in (0, 1)$ whose continued fraction expansion is equal to its base $b$ expansion for a given base $b$ , in the following sense: If $x = [0; a_{1}, a_{2}, \dots]$ ,…

math.NT2020★ 1 cited

On the smallest base in which a number has a unique expansion

Pieter Allaart, Derong Kong

Given a real number $x > 0$ , we determine $q_{s} (x) := in f U (x)$ , where $U (x)$ is the set of all bases $q \in (1, 2]$ for which $x$ has a unique expansion of $0$ 's and $…

math.NT2017★ 6 cited

Bifurcation sets arising from non-integer base expansions

Pieter Allaart, Simon Baker, Derong Kong

Given a positive integer $M$ and $q \in (1, M + 1]$ , let $U_{q}$ be the set of $x \in [0, M / (q - 1)]$ having a unique $q$ -expansion: there exists a unique sequence $(x_i)=x_1x_2\ldot…

math.NT2016

On univoque and strongly univoque sets

Pieter C. Allaart

Much has been written about expansions of real numbers in noninteger bases. Particularly, for a finite alphabet ${0, 1, \dots, α}$ and a real number (base) $1 < β < α + 1$ , the so-called…

math.NT2012

Digital sum inequalities and approximate convexity of Takagi-type functions

Pieter C. Allaart

For an integer b>=2, let s_b(n) be the sum of the digits of the integer n when written in base b, and let S_b(N) be the sum of s_b(n) over n=0,...,N-1, so that S_b(N) is the sum of…