Thomas C. Martinez

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20202026

most citedGeneralizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, II

3 citations · 3 across the 10 of their papers we have counts for

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math.NT2020★ 3 cited

Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, II

Thomas C. Martinez, Steven J. Miller, Clayton Mizgerd +2

Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers ${F_{n}}$ , where we take $F_{1} = 1$ and $F_{2} = 2$ …

math.NT2020

On Class Numbers, Torsion Subgroups, and Quadratic Twists of Elliptic Curves

Talia Blum, Caroline Choi, Alexandra Hoey +3

The Mordell-Weil groups $E (Q)$ of elliptic curves influence the structures of their quadratic twists $E_{- D} (Q)$ and the ideal class groups $CL (- D)$ of i…

math.NT2020

Generalizing the Distribution of Missing Sums in Sumsets

Hung V. Chu, Dylan King, Noah Luntzlara +5

Given a finite set of integers $A$ , its sumset is $A + A := {a_{i} + a_{j} ∣ a_{i}, a_{j} \in A}$ . We examine $∣ A + A ∣$ as a random variable, where $A \subset I_{n} = [0, n - 1]$ , the set of integer…

math.NT2020

Generalizing Zeckendorf's Theorem to Homogeneous Linear Recurrences, I

Thomas C. Martinez, Steven J. Miller, Clayton Mizgerd +1

Zeckendorf's theorem states that every positive integer can be written uniquely as the sum of non-consecutive shifted Fibonacci numbers ${F_{n}}$ , where we take $F_{1} = 1$ and $F_{2} = 2$ …