10 citations · 17 across the 10 of their papers we have counts for
8 papers · 1 filter
Sums of Powers in Large Finite Fields: A Mix of Methods
Vitaly Bergelson, Andrew Best, Alex Iosevich
Can any element in a sufficiently large finite field be represented as a sum of two th powers in the field? In this article, we recount some of the history of this problem, touc…
Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions
Andrew Best, Karen Huan, Nathan McNew +4
Two well studied Ramsey-theoretic problems consider subsets of the natural numbers which either contain no three elements in arithmetic progression, or in geometric progression. We…
The emergence of 4-cycles in polynomial maps over the extended integers
Andrew Best, Patrick Dynes, Steven J. Miller +2
Let ; for each integer it is interesting to consider the number of iterates , if possible, needed to satisfy . The sets $\{α, f(α),…
Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , with initial terms . Previo…
Benford Behavior of Generalized Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by and , every…
Geometric-progression-free sets over quadratic number fields
Andrew Best, Karen Huan, Nathan McNew +4
A problem of recent interest has been to study how large subsets of the natural numbers can be while avoiding 3-term geometric progressions. Building on recent progress on this pro…
Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , with initial terms . We con…
Benford Behavior of Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers . A set $S \subset \…