1 citations · 1 across the 3 of their papers we have counts for
9 papers
A refined Chabauty--Coleman bound for surfaces
Jennifer S. Balakrishnan, Jerson Caro
Caro and Pasten gave an explicit upper bound on the number of rational points on a hyperbolic surface that is embedded in an abelian variety of rank at most one. We show how to use…
Variations of Lehmer's Conjecture for Ramanujan's tau-function
Jennifer S. Balakrishnan, William Craig, Ken Ono
We consider natural variants of Lehmer's unresolved conjecture that Ramanujan's tau-function never vanishes. Namely, for we prove that $$τ(n)\not \in \{\pm 1, \pm 3, \pm 5, \…
Two recent p-adic approaches towards the (effective) Mordell conjecture
Jennifer S. Balakrishnan, Alex J. Best, Francesca Bianchi +4
We give an introductory account of two recent approaches towards an effective proof of the Mordell conjecture, due to Lawrence--Venkatesh and Kim. The latter method, which is usual…
Explicit quadratic Chabauty over number fields
Jennifer S. Balakrishnan, Amnon Besser, Francesca Bianchi +1
We generalize the explicit quadratic Chabauty techniques for integral points on odd degree hyperelliptic curves and for rational points on genus 2 bielliptic curves to arbitrary nu…
Chabauty-Coleman experiments for genus 3 hyperelliptic curves
Jennifer S. Balakrishnan, Francesca Bianchi, Victoria Cantoral-Farfán +2
We describe a computation of rational points on genus 3 hyperelliptic curves defined over whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty an…
An effective Chabauty-Kim theorem
Jennifer Balakrishnan, Netan Dogra
The Chabauty--Kim method is a method for finding rational points on curves under certain technical conditions, generalising Chabauty's proof of the Mordell conjecture for curves wi…