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.CO2020

Counting on Euler and Bernoulli Number Identities

Arthur T. Benjamin, John Lentfer, Thomas C. Martinez

While there are many identities involving the Euler and Bernoulli numbers, they are usually proved analytically or inductively. We prove two identities involving Euler and Bernoull…

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 $F_{2} = 2$ …