3 papers
math.NT2025
Unbounded average Selmer ranks of elliptic curves in torsion families
Tristan Phillips
Let and be positive integers for which the modular curve has genus , and let be a prime divisor of . 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 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 of elliptic curves over with an addit…