1 citations · 3 across the 12 of their papers we have counts for
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Lattice point visibility along powers of quadratic polynomials
Abraham Lobsenz, Tristan Phillips
We study the growth of the number of invisible lattice points along powers of quadratic polynomials. Let have a positive leading coefficient and no…
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.
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.
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…
Counting Drinfeld modules with prescribed local conditions
Tristan Phillips
We give asymptotics for the number of Drinfeld -modules over of a given height, which satisfy prescribed sets of local conditions. This is done b…
Points of bounded height on projective spaces over global function fields via geometry of numbers
Tristan Phillips
We give a new proof of a result of DiPippo and Wan for counting points of bounded height on projective spaces over global function fields. The new proof adapts the geometry of numb…
Points of bounded height on weighted projective spaces over global function fields
Tristan Phillips
In this note we give exact formulas (and asymptotics) for the number of rational points of bounded height on weighted projective stacks over global function fields.
Average analytic ranks of elliptic curves over number fields
Tristan Phillips
A conditional bound is given for the average analytic rank of elliptic curves over an arbitrary number field. In particular, under the assumptions that all elliptic curves over a n…
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 $ρ…
Most Elliptic Curves over Global Function Fields are Torsion Free
Tristan Phillips
Given an elliptic curve over a global function field , the Galois action on the -torsion points of gives rise to a mod-n Galois representation . For sati…