Steven J. Miller

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20142023

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math.NT2021

Connections of Class Numbers to the Group Structure of Generalized Pythagorean Triples

Thomas Jaklitsch, Thomas C. Martinez, Steven J. Miller +1

Two well-studied Diophantine equations are those of Pythagorean triples and elliptic curves; for the first, we have a parametrization through rational points on the unit circle, an…

math.NT2014

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 $F_{1} = 1, F_{2} = 2$ and $F_{n + 1} = F_{n} + F_{n - 1}$ , every…

math.NT2014

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 ${F_{i}}_{i = 1}^{\infty}$ . A set $S \subset \…