13 citations · 13 across the 5 of their papers we have counts for
7 papers
The fractional Makai-Hayman inequality
Francesca Bianchi, Lorenzo Brasco
We prove that the first eigenvalue of the fractional Dirichlet-Laplacian of order on a simply connected set of the plane can be bounded from below in terms of its inradius only…
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…
Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture
Francesca Bianchi
We explore a number of problems related to the quadratic Chabauty method for determining integral points on hyperbolic curves. We remove the assumption of semistability in the desc…
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…
A result on the analytic -invariant of elliptic curves
Francesca Bianchi
We generalise a result by Greenberg and Vatsal on the relation between the analytic -invariants of two elliptic curves whose -torsion subgroups are isomorphic as Galois mod…
Consequences of the functional equation of the -adic -function of an elliptic curve
Francesca Bianchi
We prove that the first two coefficients in the series expansion around of the -adic -function of an elliptic curve over are related by a formula involving…