Jeremy A. Rouse

activity

20072023

most citedGalois theory of iterated endomorphisms

44 citations · 123 across the 26 of their papers we have counts for

collaborators

Showing 2015Show all

4 papers · 1 filter

math.NT2015

Trinomials defining quintic number fields

Jesse Patsolic, Jeremy Rouse

Given a quintic number field $K / Q$ , we study the set of irreducible trinomials, polynomials of the form $x^{5} + a x + b$ , that have a root in $K$ . We show that there is a…

math.NT2015

The density of primes dividing a particular non-linear recurrence sequence

Alexi Block Gorman, Tyler Genao, Heesu Hwang +3

Define the sequence ${b_{n}}$ by $b_{0} = 1, b_{1} = 1, b_{2} = 2, b_{3} = 1$ , and $$b_n=\begin{cases} \frac{b_{n-1}b_{n-3}-b_{n-2}^2}{b_{n-4}}&\textrm{if}~ n\not\equiv 0\pmod 3, \frac{b_{n-1}b_{n-3…

math.NT2015

The density of primes dividing a term in the Somos-5 sequence

Bryant Davis, Rebecca Kotsonis, Jeremy Rouse

The Somos-5 sequence is defined by $a_{0} = a_{1} = a_{2} = a_{3} = a_{4} = 1$ and $a_{m} = \frac{a _{m - 1} a _{m - 4} + a _{m - 2} a _{m - 3}}{a _{m - 5}}$ for $m \geq 5$ . We relate the arithme…

math.NT2015

Three consecutive almost squares

Jeremy Rouse, Yilin Yang

Given a positive integer $n$ , we let $sfp (n)$ denote the squarefree part of $n$ . We determine all positive integers $n$ for which $\max \{ {\rm sfp}(n), {\rm sfp}(n+1), {\rm…