43 citations · 53 across the 9 of their papers we have counts for
9 papers
Hölder continuity and dimensions of fractal Fourier series
Efstathios Konstantinos Chrontsios Garitsis, AJ Hildebrand
Motivated by applications in number theory, analysis, and fractal geometry, we consider regularity properties and dimensions of graphs associated with Fourier series of the form $F…
The Number of Optimal Strategies in the Penney-Ante Game
Reed Phillips, A. J. Hildebrand
In the Penney-Ante game, Player I chooses a head/tail string of a predetermined length . Player II, upon seeing Player I's choice, chooses another head/tail string of the sa…
On cyclic and nontransitive probabilities
Pavle Vuksanovic, A. J. Hildebrand
Motivated by classical nontransitivity paradoxes, we call an -tuple \textit{cyclic} if there exist independent random variables wit…
The Surprising Accuracy of Benford's Law in Mathematics
Zhaodong Cai, Matthew Faust, A. J. Hildebrand +2
Benford's law is an empirical ``law'' governing the frequency of leading digits in numerical data sets. Surprisingly, for mathematical sequences the predictions derived from it can…
A local Benford Law for a class of arithmetic sequences
Zhaodong Cai, A. J. Hildebrand, Junxian Li
It is well-known that sequences such as the Fibonacci numbers and the factorials satisfy Benford's Law, that is, leading digits in these sequences occur with frequencies given by $…
Almost Beatty Partitions
A. J. Hildebrand, Junxian Li, Xiaomin Li +1
Given , the Beatty sequence of density is the sequence . Beatty's theorem states that if are irrational numbers with $α+…