11 papers · 1 filter
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…
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.
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)…
Local Monodromy of 1-Dimensional p-Divisible Groups
Tristan Phillips
Let be a -divisible group over a complete discrete valuation ring of characteristic . The generic fiber of determines a Galois representation . The image of $…
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…
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.