Alex Cowan

activity

20172025

most citedThe distribution of multiples of real points on an elliptic curve

1 citations · 3 across the 12 of their papers we have counts for

collaborators

Showing 2023Show all

3 papers · 1 filter

math.NT2023★ 1 cited

Murmurations and explicit formulas

Alex Cowan

Unexpected oscillations in $a_{p}$ values in a family of elliptic curves were observed experimentally by He, Lee, Oliver, and Pozdnyakov. We propose a heuristic explanation for these…

math.NT2023

A twisted additive divisor problem

Alex Cowan

We give asymptotics for shifted convolutions of the form $n < X \sum \frac{σ _{2 u} ( n , χ ) σ _{2 v} ( n + k , ψ )}{n ^{u + v}}$ for nonzero complex numbers $u, v$ and nontrivial Dirichlet charac…

math.NT2023

Counting modular forms by rationality field

Alex Cowan, Kimball Martin

We investigate the distribution of degrees and rationality fields of weight 2 newforms. In particular, we give heuristic upper bounds on how often degree $d$ rationality fields occ…