Jeremy A. Rouse

activity

20122020

X_{1} (N)

with rational

j

-invariant

3 citations · 3 across the 2 of their papers we have counts for

collaborators

6 papers

math.NT2020★ 3 cited

Odd degree isolated points on $X_{1} (N)$ with rational $j$ -invariant

Abbey Bourdon, David R. Gill, Jeremy Rouse +1

Let $C$ be a curve defined over a number field $k$ . We say a closed point $x \in C$ of degree $d$ is isolated if it does not belong to an infinite family of degree $d$ points parame…

math.NT2019

Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves

Michael Cerchia, Jeremy Rouse

Let $ℓ$ be a prime number and let $F$ be a number field and $E / F$ a non-CM elliptic curve with a point $α \in E (F)$ of infinite order. Attached to the pair $(E, α)$ is the $ℓ$ -…

math.NT2018

$p$ -adic quotient sets II: quadratic forms

Christopher Donnay, Stephan Ramon Garcia, Jeremy Rouse

For $A \subseteq {1, 2, \dots}$ , we consider $R (A) = {a / a^{'} : a, a^{'} \in A}$ . If $A$ is the set of nonzero values assumed by a quadratic form, when is $R (A)$ dense in the $p$ -adic…

math.NT2018

The density of odd order reductions for elliptic curves with a rational point of order 2

Ke Liang, Jeremy Rouse

Suppose that $E / Q$ is an elliptic curve with a rational point $T$ of order $2$ and $α \in E (Q)$ is a point of infinite order. We consider the problem of determinin…

math.NT2018

Integers represented by positive-definite quadratic forms and Petersson inner products

Jeremy Rouse

Let $Q$ be a positive-definite quaternary quadratic form with integer coefficients. We study the problem of giving bounds on the largest positive integer $n$ that is locally repres…

math.NT2012

A 60,000 digit prime number of the form $x^{2} + x + 41$

Justin DeBenedetto, Jeremy Rouse

Motivated by Euler's observation that the polynomial $x^{2} + x + 41$ takes on prime values for $0 \leq x \leq 39$ , we search for large values of $x$ for which $N = x^{2} + x + 41$ …

Odd degree isolated points on X1​(N) with rational j-invariant

Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves

p-adic quotient sets II: quadratic forms

The density of odd order reductions for elliptic curves with a rational point of order 2

Integers represented by positive-definite quadratic forms and Petersson inner products

A 60,000 digit prime number of the form x2+x+41

Odd degree isolated points on $X_{1} (N)$ with rational $j$ -invariant

$p$ -adic quotient sets II: quadratic forms

A 60,000 digit prime number of the form $x^{2} + x + 41$