T. Phillips

activity

20242026

collaborators

12 papers

math.NT2026

Upper bounds for moments of analytic ranks of elliptic curves over number fields

Tristan Phillips, Saahil Sharma

We prove a conditional upper bound for moments of the analytic rank of elliptic curves over number fields. We also prove conditional bounds for the density of elliptic curves with…

math.NT2026

Lattice point visibility along powers of polynomials

Abraham Lobsenz, Tristan Phillips

We study lattice point visibility along polynomial lines of sight and give a new proof of the Visibility Density Conjecture of Chaubey and Pandey for a large class of polynomials.

math.CO2026

On the largest strongly connected component of randomly oriented divisor graphs

Jihyung Kim, Tristan Phillips

We introduce the study of \textit{randomly oriented divisor graphs}. For each $ρ \in [0, 1]$ , the randomly oriented divisor graph $D_{ρ} (N)$ is obtained from the divisor grap…

math.NT2026

Points of bounded height in images of morphisms of weighted projective stacks with applications to counting elliptic curves

Tristan Phillips

Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite)…

math.NT2026

Local Monodromy of 1-Dimensional p-Divisible Groups

Tristan Phillips

Let $G$ be a $p$ -divisible group over a complete discrete valuation ring $R$ of characteristic $p$ . The generic fiber of $G$ determines a Galois representation $I ¨ $ . The image of $…

math.NT2025

Unbounded average Selmer ranks of elliptic curves in torsion families

Tristan Phillips

Let $M$ and $N$ be positive integers for which the modular curve $X_{1} (M, M N)$ has genus $0$ , and let $p$ be a prime divisor of $M N$ . This article gives asymptotic lower bounds for t…