Nick Rome

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math.NT2026

Poissonian correlations of $I^\pm n^{d}$ mod $1$

Chris Lutsko, Nick Rome, Niclas Technau

Let $x (n) := I^\pm n^{d} mod 1$ for integer $d > 1$ and non-zero real $I^\pm$ . We show that ${x (n)}_{n > 0}$ has Poissonian $ℓ$ -point correlations for almost all choices of $I^\pm$ when $d$ i…

math.NT2024

On the existence of magic squares of powers

Nick Rome, Shuntaro Yamagishi

For any $d \geq 2$ , we prove that there exists an integer $n_{0} (d)$ such that there exists an $n \times n$ magic square of $d^{th}$ powers for all $n \geq n_{0} (d)$ . In particula…

math.NT2024

Integral solutions to systems of diagonal equations

Nick Rome, Shuntaro Yamagishi

In this paper, we obtain an asymptotic formula for the number of integral solutions to a system of diagonal equations. We obtain an asymptotic formula for the number of solutions w…

Poissonian correlations of I^±nd mod 1

On the existence of magic squares of powers

Integral solutions to systems of diagonal equations

Poissonian correlations of $I^\pm n^{d}$ mod $1$