Alex Cowan

activity

20172020

collaborators

4 papers

math.NT2020

Conjecture: 100% of elliptic surfaces over $Q$ have rank zero

Alex Cowan

Based on an equation for the rank of an elliptic surface over $Q$ which appears in the work of Nagao, Rosen, and Silverman, we conjecture that 100% of elliptic surfaces ha…

math.NT2019

Non-Random Behaviour in Sums of Modular Symbols

Alexander Cowan

We give explicit expressions for the Fourier coefficients of Eisenstein series twisted by Dirichlet characters and modular symbols on $Γ_{0} (N)$ in the case where $N$ is prime and eq…

math.NT2019

The distribution of multiples of real points on an elliptic curve

Alex Cowan

Given an elliptic curve $E$ and a point $P$ in $E (R)$ , we investigate the distribution of the points $n P$ as $n$ varies over the integers, giving bounds on the $x$ and $y$ …

math.NT2017

Constants in Titchmarsh divisor problems for elliptic curves

Renee Bell, Clifford Blakestad, Alina Carmen Cojocaru +5

Inspired by the analogy between the group of units $F_{p}^{\times}$ of the finite field with $p$ elements and the group of points $E (F_{p})$ of an elliptic curve $E/\…

Conjecture: 100% of elliptic surfaces over Q have rank zero

Non-Random Behaviour in Sums of Modular Symbols

The distribution of multiples of real points on an elliptic curve

Constants in Titchmarsh divisor problems for elliptic curves

Conjecture: 100% of elliptic surfaces over $Q$ have rank zero