T. Phillips

collaborators

Showing math.NTShow all

3 papers · 1 filter

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…

math.NT2025

Counting points on some genus zero Shimura curves

Tyler Genao, Tristan Phillips, Fredderick Saia +2

We count certain abelian surfaces with potential quaternionic multiplication defined over a number field $K$ by counting points of bounded height on some genus zero Shimura curves.

math.NT2025

100% of elliptic curves with a marked point have positive rank

Jun-Yong Park, Tristan Phillips

As a consequence of their work on average Selmer ranks of elliptic curves with marked points, Bhargava and Ho proved that $100%$ of elliptic curves over $Q$ with an addit…